I feel like I've lost my trust in women after I've been cheated on?

My ex cheated on me a couple of months ago. It was tough for me to get over that because it was the first time anyone's treated me like that. I loved her and things ended so suddenly I didn't have enough time for closure. Anyway there's this girl who's interested in me, I met her at university. I wouldn't mind going for it but I don't think i'm fully over my ex yet, and also I keep having this sinking feeling like the same things going to happen again once we get close. Is this normal? How to I get over this?