Yes, I have had something similar, but it was a little itchy, probably because it was hot and swollen and dry. I didn't know I had hashi's when I had this. (I do have contact dermatitis and can have extreme reactions where my skin will go black and peel off - painful and yucky!)
I could not think what had caused the problem with my legs at the time, and the skin would break and weep, I thought I must have caught something, but had no idea what or how! But having just checked on Medscape, the picture looks just like what I had. I have had it a couple of times over the years.
I don't remember a problem with the eyes, but my eyelids have been very sore and pink in the past - I just thought that it was dermatitis, use aqueous cream and wait until it heals.
I am not sure if I ever went to the doctor about it.
(I had a similar reaction across my stomach when I used penicillin once, and the doctor gave me such a lecture and said that if I took it again I would probably go into anaphalaxyis - he gave me a different type of Betnovate, with an emollient carrier rather than the usual cream that I had always been prescribed - and you guessed it, I was allergic to the carrier emollient and had to use washing up liquid and a nail brush to try and get it off because it was so painful!)
I have scarring on my arms from what I thought was a painful allergic reaction to something, for which I took Ibuprofen, only to find that the blisters that were appearing were actually an allergy to the ibuprofen! - I really feel like a mess! The scars look like horrid age freckles several years down the line, so the only long lasting hurt is to my vanity! - I have to use paracetemol now as all aspirin derivatives are off the agenda.
It is amazing how much hashis/hypothyroidism can affect you!! It is no wonder that your common or garden GP can't know it all - they have to know so many illnesses that are far more common and dangerous (but I am not sure why an endocrinologist would not ask you for any symptoms that would fit the bill).
I had no idea that this could be yet another symptom of hashis!!
I hope that your legs heal up quickly!