Welcome to SI and so sorry you're here. In the JFO (Just Found Out) forum there are some posts pinned to the top that I encourage new members to read. There are other posts that are marked with bull's eye icons that aren't pinned but have a lot of great information. The Healing Library is at the top of the site and has a lot of great information.
So sorry for the loss of your father. That just adds to the stress of the situation and it's terrible that you can't lean on your partner for support at this time.
Please see your doctor and be tested for STDs/STIs because there are some nasty diseases out there that can turn into cancer and kill you. Also, if you are on antidepressants, you may need a dosage adjustment due to trying to heal from infidelity at this time.
If you can, IC (individual counseling) with a trauma-informed therapist can be helpful. It can take 2-5 years to heal from infidelity, and that doesn't include the time that it would take to heal the M (marriage). At 3 months, you've barely started and are in the early stages. Any new information resets the timer on your healing clock.
I'm having nightmares constantly about the two of them
That's your brain on trauma. I had nightmares (2-3 per night) almost nightly for 3 years. You may develop PTSD or have C-PTSD from this. There is also something called PISD (post-infidelity stress disorder) that doesn't have a true diagnosis code yet, but you may identify with the symptomology.
why I deserved all of this
You don't deserve this. This is all on him and his broken moral compass. He made hundreds if not thousands of conscious decisions to lie, cheat and betray. He didn't do the grown up thing to do which would have been discussing this with you, suggesting MC (marriage counseling) or asking for a divorce. Instead, he decided to cheat.
Self-esteem takes a hit when we find out that we've been betrayed. This really had nothing to do with how you looked. Think of all the stars that are attractive and slim that have been cheated on. Adam Levine (lead singer for Maroon 5) had an A (affair) and his wife was a Victoria's Secret underwear model.
You need to think of yourself as a BASGU - bad ass sparkly unicorn goddess. Get an outfit or several that makes you feel absolutely fabulous and wear them. Get some awesome underwear and wear them - no more granny panties. Also, congratulations on your weight loss. Another thing that I did was some I AM affirmations every morning. I found a YouTube video that spoke to me and I did did the 10 minute affirmations every day for a while. I also found a bracelet that said You Are Enough that was a reminder that I wasn't the one lacking.
why it happened
Your WH (wayward husband) needs to work on this as it was his decision to cheat. It sounds like he is a deceptive person and lies to get what he wants. For example, the AP had no knowledge of your relationship. It makes me wonder how many other times has he done this.
He needs IC to work on becoming a safe partner. If he wants to R (reconcile), then he should be in IC, get another job, provide passwords to all areas and rebuild trust with you. Additionally, any other boundaries you want to set in place should be followed.
I would also think about staying for the child. There are members whose parents have stayed together after infidelity and have said that it would have been better if their parents had divorced due to all the underlying tensions in the home.
Sorry you're here and please keep posting.