Should I be offended?

a real friend wouldn't do that. i have had very many friend problems in my life. it gets very annoying, but what i think is you should see if she is your friend or not. what you have to do is give her some space and just dont really interact for a while but keep it polite. then if they come back to you, you know that they want to be your friend and you can try again. that means that they see something in you. also, ask why you weren't invited to those other things.