I have not clue at the moment but it sounds miserable. I do think of a condition that normally affects the face, ear and also at times the nose and throat which can be dangerous. It is called angioedema and is treated with a drug like Zryec and sometimes steroids. Just a thought.
Have you seen a dermatologist? There are a lot of autoimmune skin diseases that have their own diagnosis and not related to a Sjogrens or lupus, etc. diagnosis. You may need to get a second opinion before this is over. Skin rashes are such a pain to diagnose. I had a rash that would come on my arms and swell up a lot, red, hot, looked like hives,etc. Finally saw a dermatopathologist who did cultures and biopsies and diagnosed it as Bullous Pemphoid autoimmune disease with a bacterial and fungal infection. You may be having more than one issue going on. I know the burning is miserable. My doc used antibiotics, antifungal cream and predisone burst and taper. I also had a bullae, which is basically a big blister, about 13 cm big on the back of my arm. I did not know it was there.
Now I use Momentasone cream for my arm lesions (which come seldom and not very large) plus the IVIG that I get for my Myasthenia gravis targets the pemphigoid also. Good luck. Irish