She's ashamed of you. No being harsh, just honest. Or rather, she is ashamed of herself for being with you.
Does she nag you about little things? The way you dress, the way you comb your hair, etc... ??
Here is what you should do.... since she isn't inviting you out to what she does with her friends, (claiming it isn't her place to invite you is bullshit, you are a couple not some "plus 1"), YOU have a get together and instruct her to invite HER friends. Tell her since she claims it isn't her place to invite you, you are making it your place to extend the invitation to her friends this time and there shouldn't be a problem.
Her reaction and response will tell you everything you need to know about this girl.
I'd just go ahead and dump her. Unless you like playing the role of Invisible Man in the relationship. There when she wants you to be or when she needs something, but invisible the rest of the time.