I'm sorry you are feeling so bad.
I am a little confused... are you dating A? Is he your primary partner, secondary partner, FWB, or something else? Your swinging partner?
So, he's told you he's only going to see you and is only going to fluid bond with you? How have you seen that he has met with a woman - through the site? Or he told you?
What are your relationships guidelines? Do you have any? You can bet your ass that if my primary girlfriend slept with someone and didn't tell me, I'd have a big issue, because our guideline is to tell each other when that stuff happens. But if it was one of my secondaries? Our guideline is - do tell me, but it doesn't have to be immediate. Just let me know the next time you see me, if you're sleeping with someone else. If it was a very casual FWB? Do tell me, but it's not even remotely a big deal - but DO be sexually safe.
So, those are my guidelines. What are yours, with A? Have you made them clear and has he agreed to them?
The only way you can continue in relationships with people is to communicate and be honest. If you don't see him tonight, you can't really communicate. So I say go there, meet him, talk to him. See what he has to say?
If he's making false promises, to be monogamous to you, then that's obviously not right. But, are you sure he has seen another woman? And was it actually to have sex? If it was an old friend, or old sexual partner, and he hooked up with them again, he might not think of that as being the same as 'dating someone else/new'. Speak to him!
Me: (29f) open poly
In a long-distance relationship with GF (39f)
Dating Descartes in my home country (27f)
“Peace comes from within. Do not seek it without." ~ Buddha