1. He’s avoiding you for some reason, it seems. You have to confront him about it (privately) and talk to him to find out what’s going on.
2. Well, you don’t have a SERIOUS jealousy problem, so that’s good. But you do have a jealousy problem, and we should fix that for the sake of your relationship. There must be something about this girl that you don’t like. Maybe it’s the way they act together, or that they share secrets when you still don’t feel as comfortable telling him things. Whatever it is, you have to find out. Try talking to him about it, but also reassuring him that you don’t want to restrict him from seeing her or anything like that. You simply want the jealousy to go away. Both of you can help each other through this. :)