Generalized numbness is not a noted result of low testosterone, but Hashimoto's could possibly cause it, and the dry skin is a Hashimoto's symptom. Have you been seen lately by your thyroid specialist?
Low testosterone is more likely to cause other issues, like low sex drive, erectile issues, hot flashes. trouble sleeping and depression before things like muscle wasting, and numbness doesn't even make the list. (I'd be more likely to think the low T also was a side effect of whatever condition is also causing your numbness, rather than the cause.)
BTW, if a doctor suggests you might have Covid, take a Covid test. (They're available everywhere, not painful to take, and don't cost much.) There's little enough reason to say "I doubt it" and not test. This is especially true if you live with someone else, it's unethical not to test if there is a suggestion you have something contagious.
As far as the numbness is concerned, talk with your thyroid specialist first, Hashimoto's can cause nerve problems and it does cause kind of unpredictable things. If the Hashimoto's has been ruled out as causing this by your doctor already, another possibility is some other kind of autoimmune disease. Also, when you were a kid, were you vaccinated against chickenpox? (Herpes zoster can produce shingles in adults, which usually presents as an itchy rash, but it does travel through the nerves.) Another thought is, does the numbness ease when you take Advil? (It works as an anti-inflammatory.)
These are all guesses, and probably some of them have been ruled out by your doctors already, but you were asking for ideas.
"He had sprayed some numbing medication up my nose and since then I haven't felt the same."
Hi. Then that's your biggest clue right there.
"...but they claim there's no way it could have been that."
No one can reasonably make such a claim. What they can say is only that it's extremely unlikely. Some people are hypersensitive to things that would never be suspected. Some can't eat anything except red meat, and so on.
"Not saying it was, just leaves me suspicious."
Good thinking.
"I went to my ENT doc to have some routine work done to check out my nasal airway."
I wouldn't say that's routine per se. If it's routine for you individually, then that suggests that you have some chronic condition - which is probably immune related.
"Covid"
or the mRNA vaccine.
My guess is that since everything else has been ruled out, you have a hyperactive immune system. You have Hashimoto's, that demonstrates you are susceptible to immune dysfunction. Any family history of Lupus, Sjogren's, Raynaud's, etc.?
Somewhere else you'd said you feel inflamed all over, right? So I'd want ESR and CRP for starters, then more blood tests for various cytokines --- IL1 and TNF at least.
"And Advil eases the symptoms.of electric shocks throughout my body, but not the numbness."
So now you know that the anti-inflammatory that Annie astutely suggested helps with some of your neuropathy. That's a big clue.
So altogether I'd want to do everything to be as anti-inflammatory as possible. Inflammation is not a single thing. It's a collection of many intertwining pathways. E.g., Advil/NSAIDS are anti-COX. I'd want also trying anti-LOX. Anti-IL1. Anti-TNF. For rashes, mast cell stabilizer(s). While also avoiding everything pro-inflammatory.
There is no cure for autoimmune disease, there is only management of symptoms by suppressing and/or inhibiting the immune system. So even if you were given a nominal Dx of something, you would likely still want to be anti-inflammatory.
Maybe a doc would Rx a trial of prednisone - especially since you have no known infection(s) and won't worry about immune suppression. If pred provides a quick benefit, then you taper off the pred and try some things parallel.
Merry Christmas, as much as possible, Jay.
"He had sprayed some numbing medication up my nose and since then I haven't felt the same."
Possibly lidocaine. So then:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8399637/
"Lidocaine: A Local Anesthetic, Its Adverse Effects and Management" 2021
"...the number of recorded adverse allergic responses, particularly of hazardous responses, is quite low. However, allergic reactions can range from moderate to life-threatening... type I hypersensitivity was diagnosed in 13 cases, and four subjects had an IgE-independent allergy..."
(Type I hypersensitivity is the technical definition of allergy, and that involves IgE. Non-IgE 'allergy' could involve IgG.)
Neurological effects aren't mentioned in that review article, but that's still a possibility for you individually.
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Maybe try various plant substances. Doesn't have to be only Rx meds. Also avoiding triggers.
...any virus or a vax can trigger your underlying susceptibility, then your immune system can run amok.