Forgiveness is not for the other person, just like you said, it's for you. Bitterness will hold you back.

Most of the time, some people don't even realize that they hurt you. It wasn't their intention and they may have no clue that it hurt. So, they continue on as if nothing was wrong, but if you don't forgive, you hold it in and eventually you may find a physical issue due to that anger and bitterness.