Was I so wrong for how I reacted?

I know all this is going to seem extremely immature, because it is. Please don’t be rude. But I would still like some opinions and advice on the situation.

This guy I’ve been seeing has told me he’s not talking to other girls, I told him I won’t talk to other guys, and he called me his girlfriend, called me babe and baby, all this stuff. I thought we had a good understanding and great connection. He’s taken me on long nice dates and we’ve had sex three times now.. Well the other night I forget why he even said this (we had both been drinking a little bit), but he gave me his phone told me his passcode and confidently said “go through my phone I have nothing to hide.” I said I really don’t want to and he said no, go through it. So I’m like lol ok, and I saw he had been texting girls and sending one of them heart faces, and on his dating app I saw that he recently updated his profile pictures and had messaged girls on there. I respectfully said what is this? And he instantly tried to come up with stupid lies. He said the one girl was his cousin and he tried to lie about the dating site. I told him please don’t be calling me your girlfriend and all this stuff if you’re going to do this. I definitely had an attitude but I kept my voice low and tried to still talk respectfully. And I kind of ignored him a bit and just watched tv so I could calm down a bit. He kept trying to lie about the dating site and lie about how the new pictures showed up there and saying the time stamps were wrong and he hadn’t messaged this girl only yesterday lol... so I got upset that he was trying to fool me, it was an insult to my intelligence. I called him a dick (I said it in kind of a joking way but I really regret saying it) and called him a liar. I said “please just stop, I’m not dumb and you’re making this worse for yourself. I’m over it.” He said I really don’t appreciate the way you’re talking to me and I said well I don’t appreciate being lied to. I said as long as you promise to not lie and just be honest from here on out then it’s fine. He’s like no I won’t accept that because you’re calling me a liar and not even giving me the benefit of the doubt. I’m like ok prove what you’re trying to tell me then, and he couldn’t of course. I was like seriously I’m over it (even tho I wasn’t, I just wanted the argument to stop because I knew he wasn’t going to stop making up lies about the dating site). He told me he just still wants to see if we’re compatible enough (so basically he was telling me he wants to keep his options open). He did show me he had recently ghosted a lot of girls.. and he said I bet if I looked on your phone I’d see you trying to ease into dropping guys too.

So we hugged and ended up cuddling and falling asleep. The next morning we had sex again and he bought us breakfast then after leaving, he really didn’t text me much through the day and I sent him an apology text. He told me he really appreciated it. We had a phone call too (me asking for us to talk) and he never apologized for what he did to me... he just told me if this is the way I handle issues then he doesn’t want to deal with that, but he said he doesn’t know me enough to know I always act like that, but he really appreciated my apology. But he’s acting very different to me now like he’s still upset with me.

I just feel like I deserved an apology too? And I know I was a bit immature about the situation but.... ?? What are your thoughts?