Cheating? (Really long)

In the first two month of our relationship my SO was caught texting sexual things to his ex. I broke up with him for a month but decided to get back together and give him a second chance. Well a year later and we are still together, and just recently we were on his Facebook together while he was showing me some pictures when I saw a message from a girl show up. I asked him what that was and who she was and he freaked out and said I was acting weird and controlling, so he turned off the Facebook. Now the only reason I asked him what was up was because from what I read it looks like he wrote her "hey saw you on tinder..." I've never asked to go through his personal things and I don't have a Facebook to even look at his an what he posts. But it made me really upset when he said that and that he flipped it around on me making me feel a little crazy for asking who she was. So after discussing it he said that I could look through his phone And he has nothing to hide. But every time he has asked me to look through his phone I always say no because I feel like it's an invasion of privacy and brakes our trust, but now that I think about it I feel like he knew I was going to say no to looking through his phone and he would get away with hiding something. Now it's been 4 days since this has happened and I thought I could get over it but I really feel uncomfortable with it and feel a pull to go through his phone when he isn't looking, which is horrible. So I don't really know how to talk to him about this or actually see if he is cheating. I do have his Facebook password when he let it slip the other day but I don't know if I should actually use it to look on there to try and ease my mind. I just need help because when I talk to him about it his only response is that he is in love with me and would never hurt me like that and that there isn't a relationship without trust