Since there was no committed relationship and you two didn't seem to be hitting it off very well (arguing all the time), and you were not even on speaking terms, there was no reason why she could not hook up with someone else. There really isn't any "going behind your back" about it. As you say, you weren't really an official couple.
I know this is a hard thing for you, and it is understandable that you are upset, but you need to move on because she has. It's a good time to stop seeing her...trying to start things up again aren't going to settle your differences and now you have this little thing in your history with her.
There are other girls out there that you will get a long much better with, and won't put you in this kind of situation. Forgive, forget and move on and best of luck to you.