He did tell me "I will not lie to you, we were getting close to that"
Sweetheart, cheaters lie. He lied to you the entire time he was cheating, and he knows he's busted and he feels terrible for hurting you. Why would he confess to more? If they were that close and it was purely emotional, yours will be the very first story like that that I've heard, and I've been at this infidelity thing for 3 years. It would be extremely unlikely. Please, don't assume you are being given the truth. Cheaters lie. They minimize out of shame, embarrassment, they don't want to see the pain they've caused, they just don't respect the betrayed spouse, so they lie.
How do you learn to trust? That takes a very long time. First trusting yourself - you, like the rest of us - believe the lies, believed they were faithful, believed a lot of things that weren't true. So trusting yourself is hard after an A. You need to realize that trusting your spouse SHOULD be what you can do. You should expect that your spouse isn't lying. The easiest person to fool is someone that trusts you completely. It's very easy to cheat and lie and get away with it. You did nothing wrong.
You also said the marriage was on the rocks. I hope you understand that no matter what was happening, his cheating is NOT your fault. He has very poor coping skills, and he chose a very cheap way to give himself a boost. You did not contribute to this, you did not cause this, and you are in NO WAY responsible for his choice to cheat.
Cheating has never solved one problem, ever. He was running from his unhappiness, not dealing with it.
So he says she ended it. Do you know that for certain? Have you checked the phone records and emails?
My H had an EA, and he ended it before I discovered it. I had the proof that it was him that ended it so I knew it was over and had been for several months. I still watch. I always will now. This site is littered with people that have stories of false reconciliation, stories where the cheater just got better at hiding things, stories where the A was still going after years of false R. Please, assume nothing, or if you must assume, assume he is lying. This isn't a slam of him. This is experience talking. Cheaters give tt - trickle truth. This means that the entire story comes out in pieces. This is so so so so so so common. I cannot say your H is still lying. I can say he would be alone in an EA that didn't go PA after a couple of months when OW was in the same building. I can also say that I would estimate about 10% of waywards give the entire truth from the start. The other 90% use some form of TT and continue to hide pieces that they aren't caught at. I'm not trying to scare you. I'm just trying to help you see that there very well could be more to this. If so, you'll need to be tested for STDs and such.
For now, please try to sleep and eat. If you can't eat, get some Boost or Ensure drinks for nutrition. Also, stay hydrated. Drink water. Your mind will function better with some calories and some sleep.
You'll survive, as we all have, and one day you'll be very proud of just how strong you really are.