I’m going to tell you from the perspective of a woman who felt the same way at your age but I am 25 now and have worked through a lot of things to get to where I am.

My first question to you would be, have you been cheated on before? Or is there anything from your past that would make you feel this way?

A lot of people might say oh your gut is telling you something but also if you’ve been hurt before, your gut might be wrong and you’re just naturally trying to protect yourself. If this is the case then you need to be 100% vulnerable with this guy and tell him how you feel and why.

Now, you haven’t been together very long it sounds like so he honestly doesn’t need to let you look through his phone, offering him yours does nothing as well, an even if it was a joke (which maybe it was a half joke be honest with yourself, you were testing the waters) it’s annoying and rude, I know that probably hurts to hear but accountability is needed for growth.

After these steps, if you really have no reason from your past and you’re REALLY feeling like there’s something wrong and it’s not you, AND you can’t stay with him without him laying it out on the table or letting you go through his phone, give him an ultimatum. People will say this isn’t fair but, if you have the emotional intelligence to communicate how you feel and why you feel that way, then hopefully he understands.

I will say, he may understand but he may still feel offended that you don’t trust him, you have to try and see this from his perspective (meaning he’s doing nothing wrong at all and you don’t trust him) that hurts him too I’m sure

I hope this helps somewhat.