My boyfriend "talked" to another girl when we were dating and I found out, should I break up with him?

My boyfriend went to a church camp and met this girl, cuddled with her, and had intentions on hooking up with her but did not. They started texting and flirting and making plans and he lied to her saying we were broken up. A week later he told her he just wanted to stay friends because he still loved me. I found out about this girl the day he came back because there was a video on social media of him cuddling with the girl. He lied to me and told me they were just friends and that I was being paranoid. The girl sent me a screenrecording of her texts with him and I confronted him about it and he's apologizing and saying he's sorry and does not know why he did it. It has been a week since a found out that he lied to me about everything and he keeps begging for me back and that he fucked up and won't ever mess up with me again because he realizes how much I meant to him. I wanna believe because I love him and I understand people mess up but it hurts so bad and I dont know what to do.
My boyfriend "talked" to another girl when we were dating and I found out, should I break up with him?
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