I'm posting more things that occur to me from what you've written this morning.
Lets focus on you and your horrible physiological symptoms first. The adrenaline tends to dissipate quite gradually IME and you might find you're still having these symptoms in some form or another for another 8 weeks or so. Within that period though, it is likely that you will crash regularly and need some long sleeps. Try to eat easily digestible food, such as soggy cereal or even meal replacement drinks. Try if you can to drink lots of water too, in case you get dehydrated through lack of food. It's also a good thing to try to get some exercise (I went running, but a brisk walk is just as good). If you don't feel the sleeping tablets are helping, you might find it better to do without them. It seemed important to me at the time not to anaesthetise myself, but with hindsight I wish I'd used variations of a rescue/herbal remedy.
Re. counselling, it might be too early just yet and its value will be diminished while he is still holding secrets and telling lies. Read my earlier post too, about how some counsellors have beliefs that there must have been something wrong with the relationship for this to happen, plus the relationship is the easy thing to focus on while the therapist is building up trust with the couple. Both approaches can be unhelpful if a couple is insistent that beyond the normal stresses and strains, the problem didn't lie in the relationship. Like any profession, counsellors vary in skill and expertise. I wouldn't consider one who didn't have much experience of infidelity, or who didn't take a holistic approach to analysing why an affair has happened. I'd be inclined to keep the appointment for now, but don't be afraid to pre-screen a bit and ask questions about the therapist's approach.
In your shoes, a question I might ask of the therapist during the initial session is in his/her experience, why do affairs happen? If I heard a definite "there are always problems in the relationship" answer, I'd vote with my feet. If I heard something more insightful about vulnerabilities being multi-faceted and higher in some areas than in others, dependent on the unfaithful person, then I'd have confidence I was in safe hands.
WRT to your last post, IME you know when you've got the truth, because at last things make sense. His current story makes no sense at all - and don't forget that it's highly possible they both took afternoons etc. off work. I've found that betrayed partners often overlook the lies that spouses tell about being at work at all. Many unfaithful people take secret time off work, to avoid suspicion. Sometimes they deceive their employers too and invent doctor and dentist appointments.
You are right to rely on your ILs. Instantly however I can see that there are massive clues in the way your H has been socially conditioned by his parents. I expect talking about uncomfortable issues wasn't "allowed" in his family and there might have been a tendency to gloss over conflict, or suppress emotions and feelings. This often leads to adults becoming "minimisers" about threatening situations - and allows them to pretend that everything will be alright in the end. If you reflect on how you both deal with crisis situations generally as a couple, is it possible that you have a better grip on reality and your H is someone who tells you that you are worrying unnecessarily, but it often turns out that you were right to be concerned and that if you'd taken his advice, a situation might have worsened?