Hoping you have access to a dermatologist consulting with your GP. Testing should include thyroid levels and
and iron in addition to the usual metabolic profile and Blood counts. Serum protein tests can be checked as well.
Have they tested for celiac and gluten sensitivity?
IgE blood levels would be increased with some allergies
and infections.The dermatologist may order anti skin antibodies or even take a skin sample.
A chest X-ray can point to internal causes.
Collect all of your results and seek another opinion if
you can get to a University department.