I am sorry to have to welcome you to SI.
You are going to get all sorts of replies here, and some will seem to be pushing you to D(ivorce) or R(econcile) quite forcefully. That's like those people watching a horror movie who scream, "Don't go down in the basement!" or "Get out of the building!" They're speaking from experience and their pain. SI motto - "take what you need and leave the rest."
Note: What you need may not be what you want.
What You're Experiencing:
Likely you're in some amount of shock and disbelief. You are likely to be riding the Crazy Train or here they use the term The Emotional Rollercoaser, where you go from anger to despair to love to confusion to crying to ... all in the space of minutes. You might think that you're crazy, or getting there. This is all normal. Please know that you will have to grieve the marriage that is now lost.
You need to get some control back in your life, and you need to be at least minimally healthy to do so. Here's how to start:
Drink - water or juice. No alcohol for a while because that's a depressant and you don't need any more of that right now. Also, alcohol lowers inhibitions. You might start throwing things. You might start screaming and cursing. If you do either of those things then you just might end up committing spousal abuse or assaulting the other man. You don't want to wind up in jail, pay fines, or get sued over this.
Eat - regular meals if you can. If you can't, then snack on veggies and fruits throughout the day. Smoothies are good, and Ensure, Muscle Milk, and similar products can help.
Lots of us went on "The Infidelity Diet." Where you lose more than 1/2 pound per day after DDay (Destruction Day, Devastation Day, the day we found out). Be cognizant of your caloric needs.
Sleep - Sleep? Ha! What's that? Catnaps may help short term. A full night's sleep might be out of the question for you right now, but any sleep helps. You're seeing your primary care physician so please discuss sleep with them.
Exercise - I know, right? But - some form of exercise (the harder the better) can help release the stress and it gets those exercising hormones released that help you to feel better. It also helps with the anger and anxiety.
Your wife has broken your "personal narrative." The story of our lives and how we got to where we are now. It is our understanding of ourselves and provides a backdrop of experiences. When you find out that you have been betrayed by the one person that you thought had your back and that person has also broken your narrative the result is intense emotional upset and pain. Your wife has also deprived you of your "agency." Agency is having the knowledge of your life and situation, all of the true facts of a situation, and the ability to make intelligent decisions based upon that background. Your agency is gone, decisions that greatly effect you have been made for you. This, too, is very upsetting and painful. Both together are horrendous.
Her decision to cheat is 100% on her. It doesn't matter what the state of the M(arriage) was, you were not consulted about her having an A. You had no say.
Which leads us to some of things you have already experienced:
Watch out for ---
blameshifting - "I had an A because you forced me into it!" You didn't trip her so that she fell onto a penis. Suggesting that you "forced" her to do this is ludicrous. In your case your wife has thrown the AP (Affair Partner) under the bus. He is the one that caused this.
gaslighting - from the play, "Gaslight". This is where she tries to convince you that what you have seen, heard, or experienced did not in fact happen. It is a deflection and it is done with the intent of leaving you questioning whether or not you are crazy.
rugsweeping - don't sweep this under the rug. Things swept under the rug grow big, sharp fangs and trenchant, rending claws and then someday they erupt out from under the rug and that is bad news. This results in another affair, revenge affairs, or one day 5 years from now you cannot cope any longer and are simply done.
trickle truth (TT) - where her story is "only twice, I swear on the grave of my dear mother" on Monday and two weeks later you dig more and get, "well, five. But that's all, I swear!"
Therefore, believe only 50% of what you see and 0% of what she says. She has already lost her credibility and most cheaters lie to cover themselves. Sure, they tell themselves that "I'm sparing the feelings of my Ignored Spouse!" or some other noble crap but it is just that crap. They're protecting themselves.
You need to get back some control in your life. For one thing, when she had control she really screwed that up. For another, as long as you have decided that you won't leave then you are teaching her that no matter what she does you will not leave. Why should she do anything, then?
Another SI motto - You have to be willing to lose the M in order to save it.
Yet another SI motto - We teach people how to treat us by what we accept.
Your only realistic option, if you never want to go through this again, is for her to realize that she needs to take responsibility for her actions and then she needs IC to figure out what faulty thinking allowed an A to even be an option for her. Until she does that she is still in selfish thinking and she will just continue to lie and minimize the affair and resulting devastation.
She will remain vulnerable until she does the work. The big ones APs work with to entice Wss to consider cheating are need for validation, suppressed desire, unfulfilled wishes, and latent resentment. Left on their own, WSs will come up with a convenient justification for the terrible behavior just to save their marriage.
She must do the work. You must also do the work to heal from this trauma.
I'm sorry to meet you, glad that you found us.