I'm in a long distance relationship, is he cheating?

I'm 16 years old. Me and my boyfriend have only been dating for almost 5 months. I had to move here to Washington from California last month. Ever since my boyfriend started school, things just don't seem the same anymore. (I don't start school yet) We argue everyday about something that HE did. I have a cousin that goes to the same school as him, and she has two classes with him. She has been telling me that he's going around hugging girls. In the beginning of our relationship, I told him I don't mind him having girls as friends, (but he was a big cheater before we got together) and I told him I trusted him cause i did. But he told me he wasn't gonna talk to girls at all no matter what I tell him so I said okay. And now he's telling me that my cousin is lying. So idk what to believe. But the other day he walked some girl (I don't like) to class. And I confronted him about it, he said "it wasn't even like that" so I just let it go and I told him just to stop talking to her, period. So today I woke up thinking we were gonna be fine at least I was hoping we didn't argue today. Well I tried to go on his Facebook account, but he changed his password. I asked him about it, he said he "forgot it." I let that go I was just hoping into talking to him after school. So then we were texting and I go on his Snapchat and some girl texted him, I tried to press on her name but it logged me out. I tried to log back in but he had already deleted the conversation thinking I wasn't gonna see. I asked him about it, he said she asked him something about another person that is in his class. So I let that go. I went on my Snapchat and I happen to see a girls story (he claimed he hated) with him in it. When I ask him things like this, he gets so offensive and he starts asking me if I think he's cheating. And if I say yeah, then he starts telling me how I don't see the things he's done for me and everything. He starts throwing my past back at me. I happen to feel so insecure and hurt because I've never thought he'd be like this with me. But I'm also so afraid to lose him. We've just been through so many things together that it's hard to let go of, I just wanna find out if he really is cheating on me. I don't wanna keep assuming. I don't know if I'm just being paranoid or if he really is cheating on me. I don't know how to deal with this.