While hypothyroidism can cause some tingling and numbness in extremities, I've never known it to cause anything that severe. I've also known a lot of people with much higher TSH (my own was 55+ at diagnosis) and I've never heard of anything like that.
It's unfortunate that your doctor only tested TSH for thyroid function, though, because while it's considered the "gold standard", it's a far cry from being adequate. She should also have tested Free T4 and Free T3, which are the actual thyroid hormones. Those would tell what actual thyroid function is, since TSH is a pituitary hormone, not a thyroid hormone. In addition to Free T4 and Free T3, she should have tested for thyroid antibodies to determine whether or not you have Hashimoto's.
What tests did your doctor do, other than the TSH test and vitamin B-12? If you can tell us what all she tested, perhaps we can pick something out of there that could be the culprit.
I'm not sure if you should be worried about MS, particularly, but I think I'd ask for referral to a neurologist, because, apparently, your doctor didn't test for everything and some things can be present, even if blood tests appear to be "normal"... Imaging studies are often needed for diagnosis of some conditions, as well.
It's true that most hypothyroidism is autoimmune, but there are other causes, so your doctor was remiss in not testing antibodies. She was also remiss in not testing Free T4 and Free T3, so when you have your next blood work, don't just ask for T4 and T3... ask for FREE T4 and FREE T3...
I know that sounds nit-picky, but if you don't specify "FREE T4" and FREE T3, you'll get Total T4 and Total T3 and they aren't the same tests, nor do they give the same information.
I'm agreeing with you that it's unlikely that your neuropathy is caused by your hypothyroidism. Many people have Hashimoto's for years before they're diagnosed (I think I did) and before they become, clinically, hypo, though symptoms can show up before labs actually go out of range. I'm just not convinced you were one of those.
Doctors tend to take us for hypochondriacs if they don't have pat answer to our problems. Don't let that get to you. Just keep looking for the answer...
Yes, you "can" have neurological i.e neuropathy issues with hypothyroidism, but the key is "long standing, untreated" hypothyroidism and the falling down/stumbling, etc is somewhat drastic for hypothyroidism. These things don't progress over a matter of weeks; is would take months or even years of being untreated to progress to that point, which I believe is very rate. It's also relatively unlikely with a TSH level of 11, though it would be nice to know what the actual Free T4 and Free T3 levels are.
I've never had Kaiser, but I've heard plenty about the care they provide, so I'm lucky I've never had to deal with them. I'd have been paying a lot of money out of pocket...
I agree that your neuropathy is most likely "not" caused by hypothyroidism, but as usual, nothing can be ruled out completely until it's proven for sure...
How does your doctor know for sure that your hypothyroidism is caused by autoimmune condition? Did she actually test the antibodies or she is making another assumption, just because most hypothyroidism is caused by Hashimoto's?
Did you have ANA test or any other tests that might indicate other autoimmune conditions, such as Lupus?
Yes you can have neurological symptoms due to hypothyroidism. I had plenty (some severe) due to long standing untreated hypothyroidism. I have read a case study of someone with foot drop due to hypothyroidism but that isn't a common symptom. Common causes of foot drop include a lower back condition, a stroke or tumour, Parkinson's disease, motor neuron disease, multiple sclerosis, adverse reactions to drugs or alcohol, injury to foot or lower leg.
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"The onset and duration of neuropathic symptoms is generally correlated to the onset and duration of hypothyroidism [83]."*
"The severity of neuropathic symptoms does not directly correlate with the degree of thyroid deficiency, but may be associated with the duration of hypothyroidism."*
* UpToDate - Neurologic manifestations of hypothyroidism.