Hey there. Welcome. I'm glad that you found us, but I am so sorry that you had to come looking for us. We're here to support you.
Please look in the upper left corner, at the yellow box, and click on The Healing Library. Start reading. Knowledge is power and there are a lot of very good articles written there by people who have walked in your shoes. Also, any topic in this forum that have bulls-eyes next to them you should read as well. You might have to go to page 2 to find some of them.
Next, the only, ONLY obligation that you have right now, is to yourself and your children. If you don't take care of yourself, you cannot take care of your beautiful children. You have to eat (use protein shakes if you can't keep solids down), stay hydrated (no booze please), and rest when you can. You are in as much shock right now, body and mind, as if a bus had come along and hit you. Right now, it's as if you are lying on the ground, bleeding, concussed, wondering why the ground is so much closer to you. Treat yourself with kindness be gentle with yourself.
And do make that appointment with a professional on Monday. BUT, ask that person IF they have experience with infidelity. You do not want to go to some poser who believes that unless you are June Cleaver with the spotless house that you are the root cause of this mess. The fact is that your WSO did not make a mistake. A mistake is when you put on one black and one blue sock in the dark, or you forget to put that extra quarter in the meter. He made a choice. A deliberate choice to betray you. He consciously decided to screw another woman. It wasn't force, it wasn't because you gained weight, it wasn't because the cat threw up on the carpet it was his personal, deliberate choice. Don't ever let him or anyone else downplay his decision to betray you by calling it a mistake.
Come back often for support. We're all here for you. (((hugs)))