Hypothyroidism can cause neuropathy, but so can several other conditions that often go along with hypothyroidism. One of the most common is Vitamin B-12 deficiency, if it's left untreated long enough.
Are you on thyroid hormone medication? If so, which one(s), what dosage and how long have you been on it?
My neurological symptoms from hypothyroidism include burning feet, pain when applying pressure to the soles of my feet, tingling/numbness in extremities, one eyelid drooping (ptosis), absent knee reflexes, muscle weakness, carpal tunnel, cerebellar ataxia, muscle cramps, internal tremors, severe bradypnea (central nervous system depression).
"The onset and duration of neuropathic symptoms is generally correlated to the onset and duration of hypothyroidism [83]. However, symptoms of neuropathy may be present for years before the diagnosis of hypothyroidism is made. 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.
Probably...I have Hashimoto's and my main complaint was restless legs. Not exactly tingling, but still a nervous complaint of the extremities. It went away with thyroid replacement.