I think my boyfriend is cheating..Advice please?

He puts on pictures of himself asking for returns. I know it's just likes but I think if he posts pictures of himself and girls like it then that's fine it's out his control but I don't think it's okay for him to be liking girls pictures. I wouldn't like guys pictures to me it's just unacceptable. The thing that's making it worse is he never puts anything about me and him on his Facebook. No one even knows he's with me. Also, he checks my phone, which is fine i just leave my phone out anyway and he can go on it whenever because i have nothing to hide. but he never even gets his phone out when he comes over. So him not making on that he has a gf on fb, hiding his phone away, on top of seeing other girls like, comment and posting hearts on his posts makes me feel insecure. I've asked him to his face if he's talking to girls and he said no. He swore on our unborn babies life. But I don't know what to do because I still feel like he is but I have no proof. The girls commenting stuff wouldn't bother me if he just showed that he was in a relationship. So i was thinking maybe asking him if we can change our relationship statuses on Facebook just to prove he's not hiding me or pretending he's single? Or do some digging, but I have no idea how. I need him to either prove he's not talking to any of these girls by showing that he's with me or I need to find proof that he's talking to girls because atm I don't know what to think. What should I do