I'm going to cut off a friend who I wronged first.
Why do you think this is a good choice?
That's what I think is fair, since I did something wrong to her first.
Are you sure it's "fair"? Maybe try communicating about the issue instead of just taking the easy way out and skipping town.
She really hurt my feelings and I was only doing it because I was mad at her.
It is understandable that when you are hurt you might want to hurt them so you wronged her. But you should apologize at least before you break it of and give her an opportunity to continue being friends.