I think my boyfriend is cheating on me

I’m [23F] and my bf is [21M] and we’ve been dating for just over 2 months. Now I have two events to speak of. The shorter one is I found in his Facebook activity that he was looking at a few girls profile every day or so, the last one was a girl from his work. I confronted him about it and he said that he didn’t look up his work colleagues name and that he thought she sent him a friend request but I said it showed that he searched her first name before and then he found her profile. He then apologised n said he’s deleting his Facebook and Instagram so I don’t have to be worried about him. But the thing is he couldn’t answer why he was looking at these girls… I find it weird that he’s going out of his way to solely look at girls profiles on his Facebook, a part of me thinks he looked them up and messaged them but deleted the messages. Now the second thing is he has a family friend which is his sisters old boss/bestfriend. When I met her with my partner she said hello to me but then barely acknowledged me for the rest of the conversation, she was also giving him flirty eyes. She then asked him (not me) if he’d go to two up with her for Anzac Day at the pub and then she asked him if he could help them move houses, he said he was busy both times. I asked my boyfriend about who she was and if he could remove her and he got all defensive and we argued for about 15 minutes until he removed her. I found out a few days afterwards that my boyfriend and this girl used to live together for about 2 months. My boyfriend then tells me it was over last years harvest and that he only lived with her cause she lived 5 minutes away from his work, he swears nothing went on sexually with them but I find that hard to believe with the way she was looking at him and the fact that they were two singles living together. I don’t know what to think about these situations but it’s hurting my head thinking about them.

TL;DR, I think my boyfriend is cheating on me but I haven’t found anything incriminating, he has a family friend that I got to watch out for and he’s looking up girls on Facebook including his work colleague