My girlfriend and me are going through a rocky patch. I'm mad at her for not going to prom with me.
Doesn't she get the right to decided who she wants to go to the prom with?
I know that, she has the right to choose who to be with.
Even though your relationship might work apart from this situation, it is okay to end things because she didn't go with you. You could grow resentful about this and the relationship will end anyways.
I'm not giving up that easy, I really want to go to prom with her.
That she's your girlfriend and goes to the prom with someone else doesn't bode well for the future. She should've talked to you about it first. If she wanted to break up with you, not attending the prom with you is cruel and rude.