Is everything ok or am I missing something?

So My boyfriend and I have been together for about 2 months now. I found out that last weekend he talked to his ex girlfriend for the first time in 3 years. Now I understand that it's cool to still be friends with your ex. But the thing about it is he had wanted to get back together with his ex a month before he and I got together. I don't know maybe I just am so insecure about it. Also, sometimes we don't really speak we just stare at each other. Or sometimes I just be walking down the hall or just look over and find him staring at me intensely. A few days ago he said we were perfectly matched because we could just stand there forever and just stare into each others eyes. Not that I don't enjoy looking into his eyes, it's the only way I can say I love you without choking. We go to a private school and have gotten in trouble for PDA several times before.when we were staring at each other for what had seen like 5 minutes he said "ok maybe we should stop because we'll lose control and start making out and We'd get in trouble for PDA again". Maybe it's just me keeping my guard up because I don't want to get hurt. Is the relationship in good health? I feel like it is but I just want to know what other people think.