Oh dear. I was in a very similar situation (but without the cheating, at least as far as I know) nearly 8 years ago now!
Low self esteem seems to be key in all of this, judgin by my experience of being in a LDR with a very manipulative/gaslighting man, and his constant 'liking' of crap on Facebook. More than once I also saw private messages he had sent to female 'friends' (some of which he had never even met). They were never overtly deviant enough for me to be truly justified in thinking he was cheating or planning to cheat, but they were fairly flirty and totally unrepresentative of the sort of man he actually was (he always made himself out to be a charming, benevolent knight in shining armour type, while in actual fact he was the king of psychological warfare and horribly emotionally abusive). The fact also remained that if I had so much as said hello to a male friend I would have been absolutely roasted, never mind liking someone's posts or - god forbid - messaging them!
I found it really difficult to confront him about the behaviours that upset me as he always turned it back on me and consistently made out the girls he was speaking to were going through a hard time so he was just trying to give them a 'boost' (how/why I accepted that story so many times I really have no idea). I was unreasonable, mentally ill, he threatened to dump me, etc. and my self esteem was so low and my anxiety so high at that point that I believed him. In fact, I ended up totally relying on him to feel like any sort of person at all, even a shit one. I stayed in that relationship for 6 years.
The end came for me when, yet again, I noticed him showing general interest on Facebook in some girl he had met while rehearsing with his band. Same thing happened when I confronted him about it - I was gaslighted and insulted and he continued the behaviour. And I left him. Just though 'Fuck this' and left him. It was the first and last time I stood up to him in 6 long years.
Don't get me wrong, it was hell after that for a long time. His first line of attack was pretending he had been planning to propose and had picked out a ring (hahaha). When that didn't work, he threatened to kill himself. And when that failed he resorted to saying the most vile things about me, pretended he had hacked me and seen all the 'explicit photos' I had been sending to other men (complete with examples of random women without their faces showing that weren't me, obviously, as I'd never sent anyone any photos!), then topped it all by saying he was going to ruin my life and make sure I could never get a job anywhere.
I changed my email and number and met someone else.
When my first baby was born, I made the mistake of posting a couple of YouTube videos for family, and who should pop up but him, writing 'unfit mother' repeatedly in the comments section and sending me evil messages. In the end I deleted my account, but I have no doubt that he still tries to look me up and stalk me online, and no doubt wishes me great misfortune.
As a result, I have no online presence whatsoever under my real name to this day.
The good news is that my relationship with the 'new' man is still going strong 8 years later, with two beautiful daughters, and a much healthier me.
Just do it. Get out now.