Yes, this is an EA, but I wouldn't be surprised if it was a PA (physical affair), as well, especially if they're using pet names with each other.
My WH (wayward husband) had me convinced for about two months that everyone at work called his AP (affair partner) sweetheart, and that's why his texts to her said it, too. Turned out they were sleeping with each other for about four months when I first saw the suspicious texts.
If I were you, I would:
-find an IC (independent counselor, not a marriage counselor) to work through your feelings about this. One of the hardest things for a BS (betrayed spouse) to accept is that you cannot control your spouse. You cannot make them fight for your marriage, you cannot reason with them, and the boundaries you set are rules for you to follow, not them. That means when you say something like, "I will not be in a relationship with someone that lies to my face," that means they can choose whether or not to lie to you, but if they do lie to you, you need to be prepared to enforce your boundaries and walk away.
-get tested for STDs. Right now your husband has proven that he is willing to lie to your face, lie by omission and/or minimize. If they ever had 10 minutes alone together, that's enough opportunity to physically cheat. Explain to your ob/gyn that you suspect your husband of cheating, and therefore you need to be tested for EVERYTHING. Yes, it's embarrassing, but unfortunately if you don't explain or ask for everything, you might not get tested for everything. Also, not all STDs show up at first, so practice safe sex (condoms, dental dams, etc.) if you have sex with your husband. HB (hysterical bonding) is common. After discovering an affair, many people feel this primal urge to "reclaim" their partners with sone pretty intense sex.
-if nothing was going on, your husband would be going out of his way to drop this woman causing problems, and prove to you that you're not his #1, you're his only. Think of if the situation was reversed. If you were casual friends with someone your husband disliked and it was causing problems in your marriage, would you go out of your way to lie and hang out with them? Or cool your friendship with them and reassure youe spouse?
-meet with a few lawyers and find out what a solo future would entail. Knowledge is power, and the more you know, the less fear and anxiety you'll have about the possibility of divorce and what that future looks like. Many lawyers offer free or cheap consultations for info. Meet with a few to compare what they say and get a feel for someone you would be comfortable with.
-take care of yourself. Finding out you've been cheating on makes you crazy. 70+/-% of BSs show signs of PTSD (aka PISD or post infidelity stress disorder), and symptoms include hypervigilance, anxiety, depression, mood swings, insomnia, nightmares, weight loss or gain... I dropped 30 lbs. in about a month (and I'm a tiny person). Sipping on protein shakes instead of water throughout the day helped immensely because I had zero appetite.
Lastly, check out How to Help Your Spouse Heal from Your Affair by Linda MacDonald, and Not Just Friends by Shirley Glass. HTHYSGFYA will help you ton understand the difference between a spouse with remorse and one with regret. Regret is, "I'm so sorry (because I got caught and it's annoying that you're on my case now)", whereas remorse is, "I'm so sorry (because I hurt you and broke your trust, and I need to help you heal from the pain and hurt I caused)." Not Just Friends will help you to understand how this happened. She gives an example using windows and walls, and right now your WS has opened a window WIDE open to let this woman in, while simultaneously putting up a wall between you two.
Infidelity fucking sucks, but you will be okay. Please post as often as you need, we're here to support you.