Does he trust me?

My boyfriend keeps asking me if I would let him know if any guy would DM on Instagram or as of recently he wanted to know what social media’s I had.

I told him I had a tumblr and some other ones. He asked me to screen record what it was because he didn’t know how the app looked. I did and while I was doing the screen recording he asked me to show him my messages. I found it odd but didn’t react to it. I kept thinking about it and it hit me that he maybe doesn’t trust me.

I haven’t done anything for him to not trust me. I told him that back in the past I used to have guys on me but I never paid attention.

He tells me that he does trust me and it’s just the guys around me that he doesn’t trust. But here I am thinking what do the guys matter if he knows nothing inappropriate would happen with them.

I tell him that if he trusts me, than the boys won’t matter because he knows I’m with him and only him. I reassure him many times but everything he asks or wants to see seems as if he lacks trust in me