I think recognizing this fundamental element of sinlessness in the New Covenant is where we as Christians will see the glory of the grace and truth of heaven promised through Christ. Here are just a few things that I hope will give you encouragement.

First, I believe that the glory of the New Covenant consists in this: That all true believers are perfect, holy, and blameless in the sight of God. This is the intense reality of imputed righteousness through faith, namely, that it is in the sight of God that we are declared  righteous. This is not the forensic righteousness of which reformers so often speak. That is, it is not referring to some eternal  righteousness with which God viewed us in eternity. It is not some mystically applied holiness with which God viewed us before time began. God has consistently worked out redemption in history. The Old Covenant types were always shadows of a redemption that would work itself out in history in order to bring man into eternal fellowship with an otherwise transcendent God.

This transcendence is not based upon our inability to communicate verbally with God as much as it is based upon our inability to communicate in holiness with God. The whole transcedency of God finds itself rooted in His intrinsic holiness against our intrinsic wickedness.

It is holiness in sight of God that is the crucial element of the glory of heaven. This is precisely why His dwelling place is called the holiest of holies. The Old Testament shadow of only high priests being able to enter within the physical veil was to show the more horrifying reality that certainly no one could enter within the spiritual veil. In fact Hebrews shows clearly the depressing truth that O.T. believers had to recognize:

Hebrews 10:1-3  For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. {2} For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. {3} But in those sacrifices there is a remembrance again made of sins every year.
Perfection was lacking in O.T. believers. This is certain proof that redemption had to be exectuted within history. The simple fact that the author even broaches the subject of perfection should be enough to tell us that there was something entirely fresh with the New Testament. This is exactly why he continually makes reference to something "better":
Hebrews 7:19  For the law made nothing perfect, but the bringing in of a better hope did; by the which we draw nigh unto God.
Hebrews 7:22  By so much was Jesus made a surety of a better testament.
Hebrews 8:6  But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises.
Hebrews 9:23  It was therefore necessary that the patterns of things in the heavens should be purified with these; but the heavenly things
themselves with better sacrifices than these.
Hebrews 10:34  For ye had compassion of me in my bonds, and took joyfully the spoiling of your goods, knowing in yourselves that ye have in heaven a better and an enduring substance.
Hebrews 11:16  But now they desire a better country, that is, an heavenly: wherefore God is not ashamed to be called their God: for he
hath prepared for them a city.
Hebrews 11:35  Women received their dead raised to life again: and others were tortured, not accepting deliverance; that they might obtain a better resurrection:
Hebrews 11:40  God having provided some better thing for us, that they without us should not be made perfect.
Hebrews 12:24  And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
This better covenant through the eternal sacrifice of Christ involved the accomplishment of perfection, something the O.C. and its sacrifices could never bring:
Hebrews 9:8-11  By this the Holy Spirit indicates that the way into the sanctuary has not yet been disclosed as long as the first tent is still standing. {9} This is a symbol of the present time, during which gifts and sacrifices are offered that cannot perfect the conscience of the worshiper, {10} but deal only with food and drink and various baptisms, regulations for the body imposed until the time comes to set things right. {11} But when Christ came as a high priest of the good things that have come, then through the greater and perfect tent (not made with hands, that is, not of this creation),
Reembering Hebrews chapter 10:1 we are reminded that the sacrifices could never make the "comers thereunto perfect":
Hebrews 10:1  For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect.
But the "better" sacrifices or covenant could make the comers thereunto perfect:
Hebrews 10:14  For by one offering he hath perfected for ever them that are sanctified.
The comers thereunto showed not only the inability of sacrifices to remove sin, the devastating result of this fact was that no one could enter into the holiest of holies. Yet under the New and better Covenant this is accomplished:
Hebrews 10:16-22  This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; {17} And their sins and iniquities will I remember no more. {18} Now where remission of these is, there is no more offering for sin. {19} Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus, {20} By a new and living way, which he hath consecrated for us, through the veil, that is to say, his flesh; {21} And having an high priest over the house of God; {22} Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water.
This is heaven and nothing short of it. To hope for anything better than presence with God in the holiest of holies by the precious blood of Christ is to say that the perfection and righteousness in His sight is not enough. This is why the above passage states:

"Their sins and iniquities will I remember no more." This is the glory of heaven. The glory of heaven is not the we will not remember our sins. The glory of heaven is that God will not remember our sins. It is in the sight of God that we are holy, unblameable and unreproveable:

Colossians 1:20-22  And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, I say, whether they be things in earth, or things in heaven. {21} And you, that were sometime alienated and enemies in your mind by wicked works, yet now hath he reconciled {22} In the body of his flesh through death, to present you holy and unblameable and unreproveable in his sight:
Ephesians speaks of this holiness before God:
Ephesians 1:4  According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love:
"Holy and without blame before Him" Paul says. Notice, however, the context:
Ephesians 1:3-4  Blessed be the God and Father of our Lord Jesus Christ, who hath blessed us with all spiritual blessings in heavenly places in Christ: {4} According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love:
He has blessed us with all spiritual blessing in heavenly places in Christ Jesus. What is significant about these heavenly places:
Ephesians 1:18-20  The eyes of your understanding being enlightened; that ye may know what is the hope of his calling, and what the riches of the glory of his inheritance in the saints, {19} And what is the exceeding greatness of his power to us-ward who believe, according to the working of his mighty power, {20} Which he wrought in Christ, when he raised him from the dead, and set him at his own right hand in the heavenly places,
Who had ascended to the heavenly places? Jesus Christ through His resurrection.

These are the same heavenly places where believers are blessed with all spiritual blessings. To make certain his readers understand that it is the same place, Paul emphatically declares our resurrection with Jesus Christ to the same location:

Ephesians 2:4-6  But God, who is rich in mercy, for his great love wherewith he loved us, {5} Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;) {6} And hath raised us up together, and made us sit together in heavenly places in Christ Jesus:
Paul appropriately describes this presence of the Bride resurrected with her Husband:
Ephesians 5:25-27  Husbands, love your wives, even as Christ also loved the church, and gave himself for it; {26} That he might sanctify and cleanse it with the washing of water by the word, {27} That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish.
Once again we see the theme of being resurrected with Christ and holy and without blemish before Him, hence, "present her to Himself."

Heaven is Christ in us, our Husband having consummated the marital relationship. Heaven is presence with God in the holiest of holies by the blood of Jesus Christ. Under the OT the sacrifices could not make the comers thereunto perfect. Under the NT, the sacrifice of Christ does make the comers thereunto perfect:

John 14:6  Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
Hebrews 7:17  For he testifieth, Thou art a priest for ever after the order of Melchisedec.
Hebrews 7:25  Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.
The whole context of John 14:1-6 is Christ describing how we get to the house with many mansions in that place He would go to prepare. Through Christ we come to the Father's house or heaven, the holiest of holies where God forever views us as perfect, blameless, unreproveable, without fault before His throne. This is the heavenly places in Christ Jesus. This is the New Covenant in His blood-forgiveness of sins, salvation, life everlasting, heaven, glory:
Romans 8:30  Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.
Though we feel like we are unrighteous in the sight of God, though we forget His promises and His declaration of us as justified and glorified through faith, nevertheless, if we truly believe Him we will believe He has told the truth and we will believe that truth. What manner of grace is this that would abound more than sin.