Is this cheating? How do I get over it?

My boyfriend and I are both seniors in college. I've been with him for almost two years. In recent months, I found out that he was talking to a girl he had a crush on in high school. He was telling her she was hot, texting her for months, lying about our relationship to her, but he never met up with her. When I found out about it, I told him he either had to let me read the texts to know what really went down or I'd leave him. He let me read the texts, which verified everything I said above. Then, he apologized up and down, cried, begged me to stay with him, etc.

It's been a little while since it all went down now and he hasn't done anything like that since nor has he done anything like this before. He looked her up on the Internet at one point and I again found out so I called him on that too, but he hasn't contacted her or any other women since. I still don't trust him and this also really took a toll on my self-esteem. I don't know if I'm overreacting or how to deal with any of this really. To be honest, I've been told to leave him but I know I probably won't do that, so I'm looking for ways to cope while staying in the relationship.

Has anyone had a similar experience with a boyfriend who was being disloyal but didn't necessarily cheat? How did you deal with it?