Found message from boyfriend to another girl

So my boyfriend has been "online friends" with this girl for about 6 years. Before Christmas they started talking again (their contact tends to be intermittent) and he admitted to me that they talked "as if they were both single", that he called her gorgeous, etc. I never saw the messages, at the time I thought he was just being a bit over friendly rather than out and out hitting on her, so I asked him to stop talking to her in that way. He said he was getting sick of her and was going to stop talking to her full stop. A few weeks ago, I found a recent facebook message from him to her. It told her that he thought she was really hot and asked if what they had was more than friendship, and if there was a physical side to their relationship. She lives in America so I know they haven't ACTUALLY done anything, but the fact that he seemed to be so blatantly pursuing her really, really hurt. He's deleted her, they're not talking and he claims that he was just curious about the nature of their relationship rather than wanting it to go anywhere, but if I'm honest, I don't really believe him. So now I'm stuck. He's a good guy and I don't want to overreact, but I don't know how to get over this feeling of betrayal. I feel like I can't really believe anything he says and it makes me wonder the extent of what else he's been doing. He told me he was a bit flirty at his work's Christmas party, and I assumed he meant in a "hey, you look good tonight" sort of way, but if THIS is how far his flirting goes, I'm starting to wonder if it might have been more than that. He's definitely really sorry, so how do I forgive him and trust him again, and stop torturing myself with all these thoughts?

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