I think there's actually a good chance you may be suffering from acephalgic migraine or "visual migraine" (does not typically cause a headace) commonly caused by a blood vessel having problems in the back of the head/neck, where the brain meets the neck essentially, please note I hypothesized cranio-cervical junction problems previously

I don't know for sure why you're having these type symptoms but what I will tell you is that increased blood flow and generation of new arteries from exercise will help you regardless of the cause, even if it is a demyelinating disease. Lack of bloodflow can DEFINITELY cause optic neuritis anyways, and optic neuritis has been known to be caused by medications that decrease blood pressure, and I even experienced this once in my right eye (With withdrawal of the medication that caused the lower than normal blood pressure the optical nerve's normal signal strength returned). I didn't help that I was really deconditioned and had low blood pressure anyways. This hints that to go in the opposite direction, increasing blood flow with exercise, could be a potential remedy.
Exercise certainly helps calm down the inflammation that is associated with demyelination as I posted a bit about a page or so back but I don't think you have necessarily a demyelination neuropathy nor a loss of axon/small fiber "damage" neuropathy, there is debate as to what extent I.e spinal cord injurys can heal but the peripheral nerves are actually quite good at healing themselves and can even reattach themselves if separated completely. Nerve crush is a common model in studies and these injuries can heal as well, albeit it can take some time and it takes a while for the arteries to regrow to support the growth of new nerve cells. A key point here is that there are arteries within the nerves themselves that supply the nerves with all their nutrient and oxygen needs.
However in your case I am concerned with "nerve compression", it could be out of the vertebrae known as spinal stenosis, or compression out of the ribcage and neck resulting and hand and facial/jaw neuropathy which indeed a type of neuropathy but not a type of nerve damage because the nerves have to be SIGNIFICANTLY deprived of oxygen for upwards of 7 hours in order to see axon loss.
My whole point is that neuropathy is very typically not nerve damage but a the nerves being deprived of oxygen because the arteries within the nerves are being compressed. It takes a lot to do damage real damage but the closest thing to damage that can happen is scar tissues will build up on the outside of the nerve sheath.
The myelin can also be scraped away, and we thought for a long time it might not grow, back it turns out myelin indeed does grow back.
The whole idea behind anabolism is that there are certain environments that support growth of new cells and oppose the breakdown of cells, exercise supports an anabolic environment and releases different nerve growth factors and neurotrophic factors that tell your central nervous system to grow new things and not to breakdown healthy cells, it's like growth hormone but for nerves.
Personally once upon a time I was diagnosed by nerve conduction studies with a peripheral neuropathy of an arm nerve that I was told was never going to heal, after much physical therapy and remedying the musculoskeletal problems that likely caused the neuropathy in the first place, 2 years later I had another nerve study that showed completely normal nerve function, and I no longer the symptoms of that kind of neuropathy. I should point out at this time that you should've long since had nerve conduction studies, but I should tell you that nerve compression does not show up on nerve conduction studies because it's not actual damage (loss of axons).
An electrical signal can still pass through an oxygen deprived nerve as long as the axons/myelin are still there but it's hard for your nerves to function normally when you send a conscious signal to move your hand because that requires oxygen to generate the nerve impulse, where as with the nerve conduction study the machine supplies the impulse and the nerve just conducts it.
Anyways a neurologist should be all over getting you a nerve conduction study, she will likely test your hands first. Unfortunately many of the nerves are too deep to be tested accurately but the hand ones are usually reliables. What's going to suck is if you do come back positive for carpal tunnel and such and you have a retarded doctor, all your symptoms are going to be blamed on whatever they find, when most people have some nerve damage somewhere at sometime. What they should be looking for is a global (across all nerves) decrease in conductivity, to check for a neurological disease.
But what I think you might be suffering from, thoracic outlet syndrome, cannot be diagnosed by nerve conduction studies, because it is just nerve compression, and even then the nerves are still too deep to test. It has to be diagnosed by a vascular Doppler ultrasound that will try to pinpoint where your bloodflow is slowing down (a sign of compression). There are also several office tests the neurologist should be aware of that are designed to provoke thoracic outlet syndrome symptoms. It'd be nice to rule out both the TOS and spinal stenosis, and a typical B12 vitamin deficiency that commonly causes neuropathy. But TOS is specifically for either your hands and or jaw, are your hands still burning and tingling? Does it get worse with your hands raised over your head as if you're trying to touch the ceiling for 10 seconds?
Anyways, cardio releases growth factors that cause not only the nerves to grow but cause the arteries to grow as well, a process known as angiogenesis. More arteries and increased bloodflow means less nerve oxygen deprivation and more nutrient flow to the nerves (the arteries have to carry the nerve growth factors so the nerve growth factors are useless unless there is adequate blood flow to carry them into the nerves in the first place, hence why being deconditioned cardiovascular wise leads to increased neuropathy symptoms).
Sorry for the wall of text, I hope this answers some of your questions and encourages you to keep trying some daily light walking for a while. It's okay to start easy, just walking for 10-20 minutes is great, remember you've been through/are going through a LTC, you didn't think you could start out running and not face some serious symptoms now didya
