Boyfriend flirting with another girl?

My boyfriend and I have been together for 1 1/2 months. He's a very attractive guy and of course attracts a lot of girls. I am in high school, him as well, but he is 2 years older and attends a different high school. We've attended family gatherings together and we've really just become so very close. Recently I got a text from a friend saying that my boyfriend was talking to another girl, one who went to my school. I knew the girl, friend of a friend kinda thing, so I contacted her. She sent me screenshots of the messages between her and my boyfriend. One of them implying having sex with her without my knowledge. That's his kind of humor but still... He was calling her by names of endearment. I came to him about it and the one thing he won't do is lie. He was honest about it and wasn't doing a very sincere job of apologizing. That night, he came to my house and he was much more sincere and assured me it won't happen again. This was this past week and since then I've been going crazy checking his social media and everything. I just really care about him. I'm trying to give him a second chance, but is it okay to be this crazy about it? I get very jealous and protective now. How do I regain trust?
Boyfriend flirting with another girl?
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