I would definitely also get an opinion from a rheumatologist, particularly since you have hair loss (which is just not a typical MS symptom). There is no reason why you can't go to both a neurologist and a rheumatologist.
When I first got diagnosed with MS I was having some weird things going on that were not typical of MS. They recommended I also see a rheumatologist, who turned out to be very helpful in ruling out lots of other weird random diseases--he joked that a lot of time in his specialty they get the cases that other doctors can't figure out. I had such a good experience with mine -- really interested in the "puzzle" of the diagnosis.
Getting more specific thyroid tests is smart if you haven't already.
A MS diagnosis is not the end of your life if it turns out to be MS. Some people have mild courses of the disease even after having a rough time in the beginning.
Also consider that hair loss can be a common side effect of stress -- you acknowledged that you haven't dealt with your mother's death yet. Being iron deficient can also cause hair loss.
So, have you started any new medications since this all began, like an antidepressant? I lost a significant amount of hair on Zoloft -- it really freaked me out and caused a lot of panic. Eventually it all grew back when I stopped the drug.
Hair loss often happens in cycles too. It's called telogen effluvium. Even after resolving the Zoloft issue I had another bout of hair loss a few years later. I didn't panic as much because I knew it would grow back like it did the first time.
Anyhow, there can be many reasons for hair loss. It could be coincidental the hair loss is happening with the zaps and pain. Good luck figuring things out. And seriously consider seeing a rheumatologist!!