I am not a doctor, so obviously can't give you medical advice, and if you're unconvinced then obviously you would need to do everything you can to look into other options (I did too).
But...
In case the information is helpful to you, so far nothing you've described has sounded much different from what I've gone through. I hope you'll forgive me if I write a lot here, but I see a lot of what I've gone through in what you're saying (please don't try to read it through all at once if that's a strain on you). In my experience, if one weird thing is wrong with you, it might be some other illness. If EVERYTHING weird is wrong with you, it's probably ME/CFS.
POTS, plus chemical sensitivity, plus inflammation, plus immune response, plus fatigue, plus muscle weakness, plus burning, plus extreme bloating, plus sleep issues, plus heart trouble, plus sweating for no reason, plus shortness of breath, plus extreme thirst, plus muscle twitching, plus vibrating sensations, plus trouble finding the right word for things sometimes, plus issues remembering things at the right times, plus, plus, plus... There just don't seem to be many other illnesses that affect so many different systems so severely. Most sources that deal with ME tend to just mention the same subset of core symptoms over and over, but there seem to be a lot of other weird ones that are common to many of us. And the full picture of them all together can be much more debilitating than some sources convey well.
I'm sorry about your hands. If you do have ME/CFS, then I don't think your atrophy would be from disuse at all. In fact, for me, it was the opposite. It was only the muscles I was using too much that gave out (mostly my thighs because I used them way too much trying to walk before becoming confined to bed, and occasionally my hands from typing or writing). I believe firmly that when your energy reserves are that low, there is a point that parts of the body just run out of juice and can't go on. I had my cellular energy production and mitochondrial function tested through Dr. Myhill (she has done some research around mitochondrial dysfunction in ME) around that time, and the results were pretty awful. Maybe if you don't use your hands for a while (which, I know, would be crazy hard to do) or at least reduce usage as much as possible, they'll slowly regain function. That's what happened with my thighs/hands. Your situation sounds very similar to where I was a year ago. I'm so sorry that you're suffering through that. It's an awful place to be.
If you're super ill right now, as I suspect you are given how deathly sick I felt when I was experiencing similar symptom severity to what you're describing, then even continuing to exist might count as "exertion". I know that I felt like just keeping my organs going must have been a terrible strain on my reserves sometimes. I understand what you're saying about not being able to "do anything". Even tiny things can count, though. When I was just coming back up from my lowest, I once triggered a Post Exertional Malaise backslide by trying to hold up my own cup.
And I still trigger that awful burning sensation all the type trying to use the computer.
I say this in case what you have does turn out to be ME/CFS, and in case it helps. I know for me when my symptoms were SO constant and SO severe, it was difficult for me to make connections between specific things that were making them worse. Once I had recovered enough that I wasn't in a state of constant supreme discomfort, I was able to notice that things I was doing brought the worst of it back again, and learned to cut down on those things. In particular, I know that even when I thought I couldn't possibly do any less, I was still pushing too hard to converse, research on the computer, search for information about what might help my condition, write short replies to e-mails, etc., and it was putting me in a constant cycle of getting even worse. All of that stuff counts as draining for sure. So it may be that #2 is applying to you, but that it's hard to tell since just your everyday existence right now is over-exerting for you.
Rest hasn't cured me. I am still bed bound a year later, and still have a pile of crazy symptoms and even lying down, I still can't do anything for more than half an hour to an hour without triggering symptoms. But taking more down time as the specialists recommend (i.e. lying down, eyes closed. No TV, audiobooks, music, etc.) did help to take the edge off the worst of it. So long as I stay lying down and don't do much, sometimes I feel much closer to okay. And that's a huge improvement.
I really hope that you're able to find some relief as well.
There is a decent overview of the basics of ME here, if you haven't read this one yet (the $15 is not a requirement - you can click the link to read it if you are unable to pay):
http://www.iacfsme.org/Home/Primer/tabid/509/Default.aspx
Dr. Myhill has some general information in various places on her site about pacing, management, etc.
http://www.drmyhill.co.uk/wiki/Getting_enough_rest_-_an_essential_part_of_managing_CFS
Those might not be the optimal resources for your purposes, but they're the ones I can think of right now for a look at the basics so that you can see if anything they're saying hits home or helps. I wouldn't want to throw up too many links anyway. If you're anything like I was, you probably shouldn't be using the computer now anyway (but would regardless to get to the bottom of what's wrong with you).
Good luck, and hang in there. If there's anything specific I can share about my own experiences that might help you come to a more confident decision, let me know. In the mean time, I'm going to stop typing now and gently reprimand myself for the burning I've generated in my own head and spine.