Well you shouldn't have cried at that party. You think no one saw you, but trust me, it's VERY noticable when one person breaks down. So unless all the workers were drunk, they probably noticed and we're just trying to save embarrassment by ignoring it. You do owe him an apology for that.
That being said it's EXTREMELY weird that the boss sent you an invite THEN un-invited you to a Christmas event. It's super unprofessional and strange. I find it extremely hard to believe. Not unless the company took a huge blow recently, but even then I don't feel like theyd cancel the event just so they can stay looking like they're good. It's real weird.
Prehaps your anxiety is driving your bf too crazy, maybe he wants to separate work and you now because it's too messy to mix both. After all, you did embarrass him pretty bad last time. He should learn to get over it because you are still his GF and if he wants you, eventually you'll go to events together. But let's not think he doesn't have a justified reason to want to keep it separate.
The best you can do is talk to him. Ask him why this coworker says they love him in the card and you feel uncomfortable because you don't know this person or the dynamic of their relationship. You need to bring this back up in your couples consoling to get an answer from him. Obviously you aren't going to get it by talking to him on his own. Bring up that you have reasons to believe he is cheating and tell him all of the warning signs he has given you in your behavior.
I do sense a lot of anxiety in your post. I am glad to hear you are getting help for it because it does sound like you need it.
Overall, I think it's time to consider leaving him. If he won't be open and honest with you, there is no hope for the relationship no matter what you do. If there can't be trust and he feels this huge need to hide all his coworkers he considers REAL friends from you, then I know I wouldn't want to be with him. If he's too ashamed to share them with you to at the very least introduce you guys, then I don't feel he thinks of you as seriously as you might think in the relationship.