You are right up to a point; we must be forgiven and cleansed of all our sins before we can go to heaven. God is absolutely pure and holy, and even one sin—just one—would be enough to keep us from God's presence.
But how is it possible for us to have our sins forgiven—even the ones we don't remember? It is only possible if God makes it possible—and that's exactly what He has done! God loves us and doesn't want us to spend eternity apart from Him—and that's why Jesus Christ came into the world. By His death on the cross, Christ opened heaven's door to all who put their faith in Him.
Let me explain it this way. Suppose you had done something wrong and you were arrested and brought before a judge. There was no question about your guilt, and the only thing the judge could do was order you to pay the fine—which was far more than you could ever pay. But then suppose the judge stepped down from the bench, took out his wallet, and paid the fine for you.
That is what Jesus Christ did for you. You and I are guilty before God, but Christ paid the penalty for our sins by dying in our place. And now our sins can be completely forgiven—all of them. The Bible says, "He saved us, not because of righteous things we had done, but because of his mercy" (Titus 3:5). Ask Christ to come into your life today, and trust Him alone for your salvation. Then thank God for forgiving you of all your sins.