So sorry you're having to go through this
I found out my DP did something similar about a year ago, though it was only text and email stuff and she sent him some pics in her underwear, but he never did anything physical with her(i believe him). But it broke my heart because he was the one man I've been out with that I thought would never do that to me.
We stayed together and are working through it, but if I found out they had shared a bed (regardless if they had sex) and he'd lied to me to be with her then I would be out of there. But I'm not you and I don't have your commitments.
The one thing I can honestly say to you is that counselling will help you if you can get it. It gives you someone completely independant to rant at about it and explore your feelings with before you decide what you want to do, and has helped me tremendously. Then if you decide to stay together you might want to try couples counselling to try to get over this.
I had counselling, as did my partner separately, and I'm glad he did too because his counsellor helped him see objectively how he was being unfair to me both by doing what he did and his supposed reasons for doing it.
I'll warn you - it's really hard to stay together. Even now I have days where out of nowhere I'll doubt him and have to check his mobile and stuff. But they are getting less and less, and to be honest apart from the trust issue we're getting on better than we were before, but it still hurts and it still causes rows sometimes.
Good luck. I hope things work out for you what ever you decide.