dmari, I have a 15 y.o. son, and I teach 14 and 15 years olds, and I used to be a 15 y.o boy, so here are my thoughts.
The feelings/thoughts you are describing are absolutely normal for that age group. These are the things they are thinking about everyone, not just their GF/BFs. The "why did he look at me that way?...He didn't sit with me at lunch today, why?" variety. The fact he is new to the school and this is his first girlfriend magnifies those feelings, because he doesn't know what to do. He likes the feelings, and is afraid of losing them if the GF breaks up with him.
1. Validate his feelings. Put a name to them. Ask him whether he is feeling anxious that she might break it off? Does he feel awkward and doesn't want to seem uncool? Validate that those are normal feelings.
2. Don't force him to break it off. He has to learn how to interact with girls, and the fact that he is open with you about it is great. He is willing to listen for your guidance. It isn't about man to man, it is about a human experience. As long as you are human and have had these same feelings, then you are an expert to talk with your son. Let him know what you expect from him in regards to this relationship...(treat her with respect, you do not own her and do need to let her have her space when she asks for it, etc.)
3. Give him pointers about what girls like. "You know, your GF might like it if..." I was at the grocery store with my son one day just before dropping him off at his GFs house. I told him I would give him to the money to buy her some flowers. He was reluctant at first, because there was no occasion. I said, exactly! The look on the GFs mom's face when she opened the door and my son walked in with flowers was this smile of joy and relief that her GF had a thoughtful BF.
So those are some thoughts off the top of my head. Boys and feelings are probably the hardest part of raising boys. We don't know how to identify them. There is an older book called Real Boys, which I connected to quite a bit when I read it a while back. I would recommend it. http://www.amazon.com/Real-Boys-Rescuing-Myths-Boyhood/dp/0805061835