Acid reflux does cause a sore throat but I'm not sure about the low thyroid

I have all of the same symptoms too. The low thyroid shouldn't cause a sore throat unless you have a goiter. A goiter usually has to be a pretty good size to cause any discomfort. I have one and just recently went for an ultrasound, still waiting on the results.
Acid reflux will cause a sore throat. I suffer from acid reflux due to a hiatal hernia. I get heartburn, sore throat, difficulty swallowing, etc. I take Nexium, Carafate, and Zantac everyday, which is not providing much relief though.