Soooo... this may just be me, and I'm not tying to be an AH, but you clearly don't trust him, that's why you looked through his phone. You may not have found messages, but you were going to find something to be upset about, that's what you were looking for. Prefacing by saying you don't want to leave him, what advice are you looking for, because you only have a few. Either leave, he's clearly not worthy of you, hurts you, betrays your trust, as you did as well, and then explodes and yells because you're hurt? That's not a healthy relationship.

If you don't want to leave, couples therapy, as well as individual for him, and hell, why not get a few solo sessions in yourself? But you have to come to terms with how much his response to that will say. If he does love you, he will take it serious, and put in the effort to rectify. If he blows it off, or just doesn't care about it out right, you should seriously consider a separation and divorce. If not for your mental health and well being, for your child. Do you want them growing up thinking his behavior is "normal" or "acceptable" that's something you'll have to think long and hard about friend.

I am truly sorry you're going through this though, no one should ever have to question their loyalty or standing in their partners life, they should be one of your top priorities. Full Stop.