Might a thyroidectomy resolve the problems I have due to my hypothyroidism?

Not likely. If you are having problems related to the size of your thyroid, such as choking symptoms, trouble swallowing or breathing, then thyroidectomy might help. If you are hypothyroid, your thyroid does not function well. Taking it out will not change that. Most people with hypothyroidism do not need to have their thyroid removed.