Is she really my friend?

[Anime]

From the way you describe it, no.
She is not your friend and I feel sorry for you ever associating yourself with her. She sounds stuck up and rude. She lies to you, ignores you and worst of all, she wasn't even there for you when you probably (I'm assuming, sorry if I'm incorrect) needed her most. She sounds so disrespecting. I really think you should just move on, it sounds easier said than done, and trust me, I know. I've had to do it, but everything gets better, It sounds so cheesy but it's honestly true.

As for social anxiety, I'm not sure, I've never experienced anxiety but I have been shy? (I know they're two completely different things) but maybe in some classes you could just talk to a person sitting near you (assuming your school is kind of like mine) or try, just a little, join a club out or in school to get to know people.

I honestly wish you the best of luck. This girl is not worth your time.