I don't feel you should break up with her over this. But, stand your ground, tell her what you do and do not like. If her obsession is important to her than you are, she'll more than likely move on. Good luck with it.
There are always reasons for the EX title. Something had to have gone wrong somewhere. If he keeps it up and it is making you uncomfortable, do something to let him know that you want the behavior to stop. If that doesn't do the trick, drastic measures may have to be taken. In my opinion, I wouldn't be interested in someone who has become a pest.
RE: I need help people!
I don't feel you should break up with her over this. But, stand your ground, tell her what you do and do not like. If her obsession is important to her than you are, she'll more than likely move on. Good luck with it.