Is this cheating too??? UPDATE!!!!

UPDATE: so I tried to give the relationship a second go and as much as I hated hearing most of the responses, I decided to it wasn’t going to work out with him. We had a fight and he said the words that what I believe is the reason why he cheated. He said he doesn’t love me anymore. Thinking about it, that’s why he cheated. Because he doesn’t love me. So we broke up and as upset as I am, I hope good things will come! Thank u to everyone who replied💖💖

First off, my boyfriend and I have been together for a year and he’s never given me any reason to not trust him or to think that he’s cheating! Up until he started getting weird with his phone! He started not letting me even touch it, brought it with him everywhere (wouldn’t even leave it on the counter) & would always turn the screen away from me while he’s on it! So me taking matters in my own hands, I went on it two days ago to see if there’s anything he’s hiding.

Well, I go on his Instagram and see these messages with this other girl who’s 47 (he’s 24, I’m 20).

Sorry for the messages being a little detailed 😂 but as u can imagine I was FURIOUS. I still am. Well I screenshot it and sent it to myself for reference !! I confronted him about it and at first he tried to lie until I read him the messages. The messages were from November 27, a day after his birthday. Also the days they’re talking about is when I had work until 11. He eventually gave up making excuses and said he doesn’t know why he did it and is pretty defeated on trying to defend himself. Basically, I was crying my eyes out and so was he. He was balling his eyes out because he knew he fucked up and didn’t want to lose me. Right now I don’t know what to do. I’ve made him block the girl, I messaged her on my insta and she said she never met up with him. Right now I decided not to break up with him but am I stupid for not ending it?? He seems really genuine about his apology, keeps saying sorry and said he’ll prove to me that I can trust him again. Also do you guys count this as cheating?? My boyfriend knows it was wrong but doesn’t see it as completely cheating on me as he’s been cheated on by his ex. Idk what to do & I want to know your opinion on this !! Idk if I’m stupid for not leaving him as well