I think my girlfriend and I are bad at breaking up
How are you and your girlfriend bad at breaking up?
We have a fight and we have a no contact rule, but we always seem to talk after a little while after a fight.
It's not mentally healthy for either one of you two to keep breaking up and getting back together.  If you keep getting back together, obviously you two love each other and don't want to breakup.  You should seek relationship counseling, and if your partner loves you they will agree that counseling might help.
Well I'm just fine with a little pain. I really just don't want to lose her.
It is not normal for fighting to be a part of a relationship. You should try to find someone you get along with better.