At the very least, there’s a major breakdown in trust in the relationship because she’s demonstratably lied to you and you, understandably, can’t trust her. Of course, she may or may not have actually slept with him, but I’m inclined to think that she probably has, or at least wants to, and if she hasn’t, very well may end up there after a fight.
I think you two need a real conversation, with a marriage counselor and you need to be comfortable if/when she divulges things, both with what she divulges and that it’s actually the truth. If you’re not, the relationship may or may not be irreparable, but it’s impossible to say until you’re in that spot. However, how she reacts to the idea that you should get counselling probably says more than the counseling would. Unfortunately though, the outlook doesn’t look good.
And to speak from my own experience, I was sort of on the other side of this in the past. I’d had a female friend I’d known for years and had, in fact, had interest with her but it never materialized and we remained friends. I started dating another girl, and admittedly I wasn’t completely over the first when I first started dating her, but after we got into the relationship, I was happy. However, I did maintain my friendship and we did text often, and she’d want to read them but I’d refuse because I felt it was a violation of my trust with my friend (being in a relationship with me doesn’t get you privy to my friends’ secrets, you have to be their friend too), and I never denied that I talked to her nor did I ever agree to stop talking to her. I actually had hoped that I could get them to talk and they might be friends, but my friend only very reluctantly agreed to try and my then GF just straight refused. I don’t really blame her for being jealous, but I figured being straight-forward about it very early in the relationship would be enough and, well, the fact that my friend was thousands of miles away, married, and had a kid.
Anyway, the reason I bring that up is that I do think it’s possible to have a friend of the opposite sex and not have nefarious reasons for being secretive. I probably didn’t handle my situation the best way I could have, but I definitely wasn’t cheating or inclined to cheat. The main difference between my story and the OP, though, is that there’s clearly deception going on, which means there’s probably something she doesn’t want you to know, which doesn’t leave much room other than cheating, and the dirty picture only makes it that much worse.