The symptoms you describe sound like FMS. I wouldn't know about Hashimoto's causing burning sensations. For the FMS part, you might try taking Benadryl to see if it helps. Also, lightly dry brushing with a bath brush before a shower; or try using a bath brush in a bath with Epsom salts, sea salts and baking soda (1 cup each) and follow up with a shower afterwards to wash off the salt. Lac-Hydrin or Aquafor lotion should be used on your skin.
This is a terribly annoying symptom, I sympathize.