She sounds a bit psycho to me. Do you know any of her friends? If you were my child, I would try to get you to dump her...but I don't know you so I can't say anything.
If she is like this now, what things about her are going to come up in 5 years? I think it's a freaking strange thing for a normal girl to do...though she could be amazingly insecure.
Definitely, tell her that you are not happy with it. I would be p*ssed if one of my daughter's did something like that. It's just weird.
I'm sorry, maybe I'm just old school. I wouldn't compliment her on it. I would remain really cool and level-headed and just let her know that it upsets you. If she does it anyway when she knows that it upsets you, I would rethink the relationship and possibly find another girlfriend.
If you are at the point where you need couple's counselling and you aren't even married or living together, she is the wrong wrong wrong girl for you. Why don't you ask your mother what you should do. If you are afraid to tell your mother, what would you tell your future children?