I have had dry feet, neck, chest, scalp, face, shins, lips, eyes...
I have read that allergy meds combined with Zantac or Nexium help as well as the thyroid hormone. Read the post here about Hives and Hashimoto's.
I am using Vaseline, which works much better than lotion.
I have also suffered many years from peeling lips, only recently connected that to my Hashi's. I haven't had it since they took out my thyroid (cancer) and nothing really helped my lips.