Sorry to hear that you are struggling and hurting. I see that you are not a new member, however, I'd still suggest reading "Mia's Withdrawal Guide" which is pinned to the top of this forum, which is the best place to start regarding that specific issue.
I'm not a mad-hatter, and that always puts a unique spin on recovery, however I'll share what I can.
I think you hit the nail on the head when you said that you felt rejected in the marriage by your spouse, and now feel rejected again by your AP. That's a lot of processing to deal with. But here is the thing. You put your love and devotion in with men who weren't capable of loving you back. In fact, in the case of the AP, you pretty much went in with the full knowledge that this wasn't going to make things BETTER, right?
At the end of the day, the way to get "over" the AP involves coming to two realizations. First, you have to realize who they really are. Anyone that is willing to go into an illicit affair with a married woman is, pretty much by definition, not a person with integrity, not an honest person, and no matter what they say, they certainly do not "love you" or care about you in any way. Why? Because if you really love and care about someone, you don't encourage them to lie, you don't help them tear their family apart, you don't sneak around, and you don't participate in anything that would hurt them. Those are things you do when you DON'T care about someone. That's a hard truth in life.
The second realization is who YOU are. Does lying make you feel good about yourself? Does sneaking around to see the AP make you feel special and beautiful? Do you hope one day your kids will know love with a cheating affair partner just like you do? Do you think about the day you get to tell people how you met and how wonderful it will be to tell them how you cheated on your spouse with this "wonderful" guy? I doubt it.
Look, your husband drinks to excess. That's not because he loves the taste of booze. It's because he has a hole in his heart and soul that he just can't fill, and he can't fill it because he doesn't love himself enough to think better of himself, to be a better person. He's not capable of loving you because he isn't capable of loving himself.
Sadly, when he cheated on your, he inflicted trauma on you, and now you have a hole in your heart as well. And you are trying to fill it in much the same way he does. You see how that worked out for him so far. How is it working out for you?
You get over the AP when you learn to love and respect yourself. When you realize you are worth more, and deserve more in life to than hitch your wagon to a cheater.
Here's a hint. You ARE worth more. You just feel it at the moment. And that's understandable. You were betrayed and hurt, and sometimes we just need to "sit in it" for a while, to feel the feelings and feel the hurt, it's part of the grieving process. Give yourself some grace for that. But at some point, we get off our asses and wake up, and realize that we can either go down the same rabbit hole (full of rabbit shit) that our betrayers went through, or we stand up, dust ourselves off and realize that we don't need anyone to complete us. That we're worthy of love all on our own. And we decide to be good people, not because it's the right thing to do, but because it's who we want to be.
Affairs cannot survive honesty. So get honest with yourself, and learn to love yourself again. Lots of good folks here that can help with that.