Overreacting to him texting a girl?

I’ve been dating this one guy since the beginning of the year. We were honestly going really slow bc he was being extra cautious since he had a daughter. He ended things 3 months ago bc he felt as if he wouldn’t be able to introduce me to his daughter. Well a few weeks later, he started texting me and things just fell into place. He introduced me to his daughter and has even called us two his girls. He recently just bought a house and I’ve been helping him move in all week and have been seeing him every day.

He would occasionally leave his phone out on the counter and since I was standing there I’d always notice this one girl texting him. He’s taking a few classes together with her and she has asked him previously if he wanted to carpool to class with her which he said no. It started to bother me bc she would always text him. I would joke around about it with him until he got annoyed. He told me he’s not about that jealous sh*t and that she’s just asking about school and that she’s been a friend prior and that I have nothing to worry about. He got upset with me and explained more that he doesn’t play that jealousy game. We actually went over to his friends house who are all married and he told them that I got jealous over that. I had to take a step back and realize it was pretty silly and maybe I did overreact.

He’s always treated me right. He actually told me a few days ago that he loved me, which he’s never said before. He continued to say it multiple times after. Like I have no reason to overthink it but I just do. It obviously did bother me but at the same time he’s so mature I know he doesn’t do anything like that. He used to tell me he doesn’t have the time to just date around or waste his time, so I know he’s serious especially after he told me he loves me. The issue is he’s a super friendly guy and a social butterfly. What do I do???