Consider lyme testing in that case. It's amazing the doctor's give out thyroid hormone but take no real interest in why not enough tyroxsine is being made in the first place. When it is overworked they often destroy the thyroid completely with drugs or cut it out leaving a person reliant on tyrosine for the rest of their life. It makes sense from a business perspective because the person has to be drugs.
If you can, see if you can find a naturopath/nutritionist and get some lyme tests done.
All I have confirmed from diagnostic tests is that I have an autoimmune disease (lichen sclerosus) and consistently low/out of range FSH (folliclue stimulating hormone) and sex binding globulin (SBGH). AS well as those allergies I mention. It is interesting you have a hay fever allergy. Allergic reactions and sensitivities can be caused from lyme disease which is why it's so important to get tested. Where I am the doctor's treat it as a tropical disease and are very dismissive of it, despite the fact diagnosis of lyme is on the increase and new strains are being found all the time. I do find it odd that my lips improve from no gluten in the diet.
I know this may all sound a little far fetched but until I'm tested of these things I will consider them a possibility. There is also the issue of toxicity/deficiency, both environmental and dietary which can have a massive impact on skin health and overall health.