OK so yes you messed up, but you should be able to get out of this one. I'm going to get a little deeper on this one and say that the problem isn't Myspace but it is you. Women tend to think the world is exploding when something small happens.
Right now she is imagining herself with you for the rest of her life. And you just showed her that this is your personality and she will have to put up with these kinds of things for the rest of her life. So removing Myspace doesn't take care of the problem. You will always be confronted with women flirting with you (in the workplace, on Myspace, on the street, on guys nights out). It is the way of life.
So you have to prove to her that this was a completely isolated incident that hasn't happened in the past and won't happen in the future. You can apologize until the cows come home (sorry Oklahoma tendencies showing there), but the apologies mean nothing past the first or second one. I can almost guarantee that she will look over this slip up, if you prove to her that it is in fact, a slip up and is not your M.O.