Does my boyfriend think I'm cheating?

No, I don't think he thinks you're cheating. I think he's just a little bit insecure after being cheated on before. It's normal for anyone to feel like that. I've been cheated on, so I know how it can affect you going into other relationships. It's really hard to trust someone right away because... for me, at least... the idea that I was played like that just makes me sick. And I would just never want that to happen again. I think he's into you, but he's just not over things yet.