Do you think you will go to heaven because you are living a good life?

I have heard that Christianity is different from all other religions in that you don't have to work your way to God, but where God did the work to bring you to him.

If you could be saved by "being a good person", then what is the meaning of the cross?

If righteousness come by the law, then Christ is dead in vain
--Gal 2:21

There are basically two ways to be in right-standing with God.  One is to lead an absolutely pure and sinless life, and the other is to accept God's gift of salvation.  In your case, we should probably explore option "2".

The Bible says:

Now to him that worketh is the reward not reckoned of grace, but of debt.
But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.
--Romans 4:4-5

So you must be clear on what basis you expect your salvation.  If you expect it on the basis of what you have earned, like a paycheck that is owed to you at the end of the week, then you will get what the Bible says,

The wages of sin is death;
--Romans 6:23

But if you accept salvation as a free gift for those who repent and accept it by faith, then you will get that.