It's late in the game for me to reply to this, but, as a hypothyroid patient, I would not want to risk having hyaluronic acid injections to my face. This would not be for autoimmune reasons but because HA is responsible for the accumulation of mucin beneath the skin which leads to hypothyroid myxoedema:
Hyaluronic acid is the major glycosaminoglycan that accumulates in myxedema. Its hygroscopic nature allows it to swell to one thousand times its dry weight when hydrated. Mucin deposition involves not only the skin but also the tongue, myocardium, kidney and most other organs of the body.
Safer, Joshua D. Thyroid hormone action on skin, Dermato-Endocrinology 3:3, 211-215; July/August/September 2011; ncbi.nlm.nih.gov/pmc/articl...
Personally, I would rather have wrinkles than myxoedema of the face.