Okay tell me if I’m wrong

So my boyfriend and I aren’t near each other he’s back in NY and I’m home with family I’ll be moving down there soon and i have his social media such as passwords and whatever and he has mine we been together going on 3 years December 19 and I’m a very very loyal girlfriend I haven’t cheated once I don’t talk to any of My old guy friends or anything like that I don’t talk to many female friends because to much drama can’t stand it half the time but anyways it was this one night I was on the phone with him and I log into his Snapchat to do his streakz I wasn’t looking for nothing I wasn’t expecting anything I log into it every night just to do his streaks because when he gets off work he go to sleep and so I do them for him but this one night I’m logged in and there this message from this girl so I checked it out thinking it was like a shout out but it wasn’t it was her checking to see if they’re still meeting up I was like what so then I slide up and read from the beginning and guess what I see NUDES

I get mad and I slide up more I come to find out they have been texting for a long time about since the beginning of October so I hang up and call my sister freaking out she was like call him and tell him so then I do it took forever for him to answer but when he answered I said WHAT THE FUCK he was confused i was like who is this bitch and I was just freaking out on him and blah blah blah I’m still

With him because I truly love him a lot and from my understanding this is his first time doing this but my question is am I wrong if I don’t trust him because he thinks it not fair when honestly your the one who done messed up so there for I don’t trust you at the moment