I don't know what to do anymore

So I have a boyfriend and we're currently dating for about 5 months now. I met him through my cousin. He is basically my cousin's best friend. I live with my cousin so she always told me that me and him had similar interests, so one day we just began texting and stuff. We arranged a visit and soon we became friends, it weren't that long until he asked me out and I obviously said yes. Then when wr started dating I always felt anxious and nervous, I thought it was because I weren't really used to dating that much. After about a month I would always visit him and each time I did, I wished to just go home. I felt awkward being hugged or held, whenever he talked about cuddling I would dislike the idea. I thought I just needed to get used to being in a relationship, so I ignored my feelings. About 3 months then we had a fight since I couldn't answer him when I was sleeping over at a friend, he got angry since I wouldn't text much and because I messaged late. We eventually talked it out, but not without bringing up other problems. Problems like he can't take a simple joke or something. He takes everything I say so seriously. If I would make a joke or tease him then he just look down and say he's fine. Each time we fight I would feel awkward. We recently also had another fight about him not being able to take a joke. We never talked it out, since he's the type to bring up old problems again that had already been resolved. I don't know how to feel about him, since I can't be myself in front of him. I really love him, but I sometimes think I'm not ready for this relationship. Since my cousin and boyfriend is so close, they do everything together sometimes and I feel just so insecure. She's so pretty and I was told that he had a crush on her at a time. What if he still likes her? She told me that she made a face in front of him as a joke and he apparently said that the face she made was hot. He even covered his pants, so I don't know if it was joke, but it made me feel so insecure. What's worse is that I also made that type of expression in front of him, also as a joke, but he never said it was hot or anything. He never gave any comment on it or reacted. I just feel so confused about him, since I don't want to leave him but I don't want to be near him. What should I do?