Yes, you can be sure God has forgiven you, and that someday you will go to be with Him in heaven through all eternity. And God wants you to have this assurance, because He doesn't want you to be filled with doubt and insecurity. The key is to realize that your salvation doesn't depend on you and what you have done; it depends only on Christ and what He has done for you.
Suppose for a moment that you were very poor—even penniless. Because you were so poor, you wouldn't have very much hope for the future, would you? But then suppose a very wealthy person came along and took pity on you—and suppose he told you he was going to open a bank account in your name with more than enough money to meet all your needs. Would you ignore it—or would you accept it? I think you know the answer.
In a much greater way, this is what Jesus Christ has done for us. In ourselves, we are poor—spiritually penniless because of our sins. But on the cross Christ paid the penalty for our sins, and now He offers us forgiveness—completely and fully. The Bible says, "the blood of Jesus, his Son, purifies us from all sin" (1 John 1:7). Think of that: Jesus didn't pay the price for part of your sins, but all of them! Once you realize this, your faith will grow and your doubts will fade.