Hi OP. I'm so sorry you are going through this.
Something very similar happened to me in January so I completely understand the emotions, the confusion, the pain and the plain old disbelief that you are feeling today.
With regards to messaging the OW - please consider very carefully whether you really want to hear her answers. She might tell you nothing, she might tell you everything. She might even make things up to hurt you further.
I can't tell you not to message her, because I did message the OW in my situation. I just had a complete need to know the truth from her point of view. I'm still not 100% sure I got that, but - luckily for me - she wasn't/isn't an obsessed lunatic, just a lonely bored woman who did nothing to cause any more trouble than her messages/naked photos had already caused. I have to warn you that I have heard of some OW who, when confronted, enjoy being as spiteful as possible. I really don't think you need that sort of reaction today do you?
Also, to echo others, do nothing until your mind clears. Nothing except for making H move out for a few days to give you space. Tell the DCs he's away for work if they ask. I would say yes to counselling - Relate will get you in for an initial assessment appointment fairly quickly but you will then have to wait to start regular sessions (this was my experience anyway). Whether you end up working through this or not, I would still recommend talking to an independent counsellor. They will also only charge you what you can afford to pay.
The desperate mind fog you have today is temporary - I promise you that. Time will help you to think properly & also make it clear to you whether you want to work on the marriage or not. Please don't rush anything, this is your life. You have as long as it takes to decide the best way forward for YOU.
You do need H out of the house for now. That is important. You can't think properly whilst carrying on "as normal" and whilst he is there and able to manipulate you daily.