I [22F] found out my boyfriend [21M] was texting other people

I (22F) found out about a month ago that my boyfriend (21M) of two months had been talking to other people while we were together. He was also watching and paying for porn. The hardest part was going through his phone and seeing everything for myself. There were messages where he was asking other people to meet up, and honestly, the only reason nothing happened (from what I saw) was because nobody responded. Those messages are burned into my brain, and I don’t know if I’ll ever forget them.
When I found out, I told him I would give him a month to prove he could change before deciding what to do. Since then, he has been much more open. He’s let me go through his phone whenever I’ve asked, answers my questions, and from everything I’ve seen, he does seem to be doing better.
The problem is… I don’t feel better.
I have this constant feeling that he’s hiding something. We’re long distance, so at the end of the day, all I really have is his word, and that’s the one thing I’m struggling to trust. Even when everything seems fine, my mind goes back to what I saw on his phone. I find myself bringing it up a lot, and I feel guilty because if he really is trying, I don’t want to keep punishing him for something he’s already admitted to and is trying to fix.
I’ve known him for almost a year, and I had a huge crush on him for months before we started dating. I love him deeply, which is why this is so hard. If I didn’t care about him, I probably would’ve left already.
I don’t really have anyone to talk to about this, so I’m hoping for some outside perspectives.
For people who have been through something similar:
Is it actually possible to rebuild trust after something like this?
How long did it take before you stopped feeling anxious all the time?
Is what I’m feeling normal after only a month?
At what point do you know you’re giving someone a fair chance versus just holding onto hope?

I’m really torn between wanting to make this work and wondering if I’ll ever truly be able to trust him again