Should I give up on her?

First of all: are you SURE you want to make it happen? Because to me, she doesn't sound like a very nice person. I personally don't think she's right for you. If she keeps making fun of you in public and stuff, and is rude like that... why would you want to be with her? She's just going to continue doing that. And sorry to be harsh, but it sounded like she was flirting with the other guy too- trying to get his attention. Sorry, but you should rethink this, and be 100% sure that you do want to make it happen with her. To me it sounds like a waste of time on somebody who isn't worth it...