I'm wondering what made you decide to break up. Like someone said, you probably could have needed couple's conseling.
We only hear your side of the story, which is, you definitely know, you aren't going to be a couple. Something made you decide this, but could you get over it? Are you afraid to make it a permanent commitment? Afraid to get hurt?
In a way this sounds to me, you're not sure. Now that you added the info about mutual agreement on not sleeping with others, I'm thinking is this what bothers you actually. You don't usually get to ask for a permit to cheat on someone and then possibly get back like nothing happened.
You're insecure about her now, not knowing if she is seeing others. It seems to matter to you.
In my opinion you need take a good break from your ex, so you both can work this out without getting influenced by other. But don't get involved with another yet too romantically or physically.
I'm not saying you shouldn't get acquainted with a new person either, but you shouldn't rush it. It could become a disaster, if the new gf will have to be your therapist about your previous relationship. It's not very easy to convince women, that it really is over.
