What if our sin has separated us from God that we can't restore that relationship? Will the good we do count for salvation, or will we die in our sins?

Let me answer the points in your question with some facts.

Sin has separated us from God. The bible says, “For all have sinned, and come short of the glory of God;” (Rom 3:23).

We cannot restore that relationship. We never could and we never will be able. You see, sin is in our nature. It’s not our works or efforts that is the issue, it is us ourselves. It is our very nature that is at enmity with God. The bible says, 

Rom 8:7 Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.

No good works or efforts that you do, to appease God or try to earn favour with Him, will count for anything! Again, the problem lies inside of us, inside our very nature as humans.

So then, what is the answer to your question? If we cannot do anything to find peace with God, how can we be saved? Well, the bible gives us these answers too.

God has provided us with grace through Jesus Christ. The answer is to believe in Jesus, the Son of God. Jesus willingly suffered and died in our place, and His blood has paid the debt for our sins. God took the work that Jesus did on the cross as if it was us who died there for our sins. The righteousness of Jesus Christ is imputed (accredited) to us. Have a look what the bible says about this,

Eph 2:15 Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace; 16 And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:

That sin nature in you, that is at enmity with God, has been abolished by the cross of Christ. If you believe in the gospel of Christ, and you trust in His cross to save you, then God removes that nature in you and justifies you completely. This is a free gift. You don’t work for it, you don’t deserve it, you cannot earn it or trade anything for it. God gives you justification freely if you believe in His Son, Jesus Christ.

Rom 4:5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.

Rom 4:24 But for us also, to whom it shall be imputed, if we believe on him that raised up Jesus our Lord from the dead; (25) Who was delivered for our offences, and was raised again for our justification.

Rom 5:1 Therefore being justified by faith, we have peace with God through our Lord Jesus Christ: (2) By whom also we have access by faith into this grace wherein we stand, and rejoice in hope of the glory of God.

So, can you see. Salvation has nothing to do with your actions or what you do. It is all about faith and trust in the cross of Jesus Christ. God frees you from your guilt and your sins by His own decree, having declared that we can have peace with Him if we believe in Jesus.

1Cor 15:1-4 Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; (2) By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. (3) For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; (4) And that he was buried, and that he rose again the third day according to the scriptures:

I trust the advice from the bible gives you hope and an answer to your question. There is no other way to be saved except by placing your faith in the work that Jesus did for you.

God bless.