My Boyfriend’s Text Convo, How To React?

I would like to start this off by saying that my boyfriend has never cheated on me or done anything like this before that I know of, we have a very open and honest relationship and we’ve been together for two years and I trust him, This is not a question of whether or not he’s cheating, he would never cheat because he’s been cheated on twice in past relationships.
i am always on my boyfriend’s phone because it runs on android and has games and apps. We’re very close and talk all the time, we have some really interesting conversations and most of them are over text. Sometimes I go back to old texts we’ve sent each other on his phone and we look at them together. I went to do this one night and when I read the most recent texts i didn’t recognize them or remember sending the messages at the bottom. I scrolled up and saw that he sent one saying Mikayla and I was really confused, it was then I realized that, this wasn’t between me and him.
I’m completely against reading your boyfriend’s messages or going through their phone. But once I’d seen them I just couldn’t help it.
These are some of the messages:
One night-
Him: Goodnight Mikayla, sweet dreams
Another time-
Him: Aww, you really texted me )
Her: Yeah? lol
Him: It just makes me happy )
Him: You’re like the coolest person I’ve met this year, you know that?
Him: I feel like I annoy you sometimes :/
Her: You don’t annoy me sometimes I’m just in a weird mood
Him: i dont like when you are, it makes me in a not good mood :/
There was more but, I can;t give it verbatim..
Keep in mind, he’s only known her for like, a couple weeks maybe, and they only have one class together
I just, don’t know what to do about it. First off, a lot of his friends, and I mean the vast majority, are girls. And his exes, almost all of them, all started out as friends. Even me. And he sent a lot of texts that were like the ones he sent me when we started going out. Nothing gooshy or relationship-like, but still, it makes me uncomfortable. And I’m not a jealous weirdo. I’m friends with two of his exes, really good friends with one and I’m always nice to his friends even if I don’t like them. This just makes me feel uncomfortable
But how can I tell him without him knowing I got those from his phone? I don’t want him not to trust me
I dont even go near his message anymore when I’m on there because I dont wanted to be tempted
what should i do?