Should I give up on her?

I've dealt with things like this before, and with my own experience I wasn't able to make it work but maybe you can. She makes it obvious that she does not like you, but she doesn't want to hurt your feelings. She likes the other guy, and tries to show off in front of him by making a fool out of you. I would give up on her for your own good. It's better for both of you because she doesn't really like you, so you'll be saving yourself the embarrassment and save her from having to pretend to like someone she doesn't. But, if your insisting on making it work, then try to talk to her. Tell her you want to make it work, and see what she says. Be nice to her, but not overly nice because that might get on her nerves. Be somewhere in the middle of Nice and normal. Talk to her, and see what she wants from you. Then, tell her what you want from her. If it can't work, then it just can't and unfortunately you'll have to give up. Best of luck, and I hope your able to work it out :)