Break Up time?

My current boyfriend isn't over his ex. She was his first girlfriend. They dated for 3 months but he said she found someone else at college and he thinks she cheated on him. Her college is an hour and a half from his and mine. She has a bf at college. I saw her Facebook and it looks like she's always constantly posting about him. My bf said he visited her and his family over spring break and they talked and agrees to be friends that they'd text once and a while. She texted him yesterday asking "what are you doing tonight?" He ignored it and she then texted, "(his full name), helloooooooo?" and he said, "getting drunk and having sex." That's what we did. I found this conversation because I snooped on his phone last night when he was sleeping. He said he was upset for months when she broke up with him. He told me his mother cheated on his father and he lost all respect for his mother but he still loves her. He tells me he loves me. And that he doesn't want me to go anywhere like not to cheat. I told him I'm not going anywhere if he doesn't go anywhere. The other text messages I saw between them were him asking if she remembers when they played pool and had sex before someone or people came. I don't remember what she said. What do I do? I don't want to break up with him I love spending time with him he's obnoxious and funny I fell in love with him for a bit when our relationship was going great but he told me he's going to be friends with his ex and I got mad and lost trust. He got mad because he knows I can't trust him anymore. He told me the reason he told me in the first place was so that I don't have to worry yet I did worry. It caused me to be upset. So I know from snooping on his phone, he still texts her. I told him he can text her as a friend but he shouldn't visit her or her family like over the summer. What do I do? 😞