Well OP, sounds like your situation is kinda confusing on a couple of levels.
First, it is not clear how long you and Mike were back together for after the "break". A single day or something?
Second: it doesn't matter that Mike cheated. This is about who you are as a person. This is about your character - not Mike's.
Third: things seem strained between you and Mike to begin with, hence the break. On top of that is the fact that you're LDR, which doesn't change any of the facts but does add an element where even though you're in a relationship the sense of connection is strained. And when Ryan made his move on you, there was some conflict on your part - i.e. you responded. In other words, I think you're confused about exactly what your feelings are for Mike.
OP, I don't know what to tell you. All you can do is tell Mike you're sorry. On the other hand, maybe this is a sign that the relationship bond you have with Mike isn't strong enough and really you just need to end the relationship. So on your end you have to decide if you're going to stick it out or not.
Then there's Mike. Same thing goes for him. His cheating past is, well, past. It's a past issue. It doesn't matter right now. He has to decide the same thing as you - whether or not to stick with this relationship.
For your future: you see how easy it is to get yourself in a bad situation. Ryan might not even give a single shit about you. Did he even ask how you were doing and dealing with the breakup? Doesn't sound like it. Sounds like he just wanted to see if he could get some sex from you. Regardless of Ryan's intentions, you now have a real life lesson of knowing that when the flirty shit starts you have to shut it down right away if it's inappropriate. Next time someone starts flirting with you and it's not appropriate, make sure you don't encourage the situation by flirting back. If necessary, tell someone to back off if the flirting is too heavy or they're not taking the hint. And if someone moves in for a kiss, immediately stop things and leave.