have you tried eliminating all grains from your diet for a limited amount of time, 1-3 weeks to see if there is any correlation?
Quite a few people with skin problems that include EC, Eczema, Psoriasis, Seborrheic Dermatitis , acne, etc improve significantly after elimination of all grains and all milk, or at least elimination of all grains with gluten and all products with lactose (milk sugar).
That would definitively be the first thing I would have seriously tried if suffering from any chronic skin problem.
The good thing is, if there is any correlation, you would maybe see some improvement already after 3-10 days, and that would give you an extra push to continue with the same diet.
By the way, the first 3 -10 days are the most difficult, cause we are often addicted to that kind of food, and it takes at least 7-14 days to quit cravings.
Usually, after the initial 14 days, most cravings are gone, and you are well used to your new diet.
The first 3 days are the most difficult, that is where most people fail with a new diet, if they are not motivated enough, or they are not used to selfcontrol.
If there is absolutely no improvement after 10 days, that would still not mean you have no problems with grains/milk, it would still keep an open possibility that grains/milk may still be a problem, but there was no improvement because you were still in contact with something else, something like eggs or nuts or Sugar or food additives , and as long as you consume the offending food(s).... it keeps triggering skin death and peeling.
Quite many hypersensitive people today react to more than one food item, making it difficult to find what it is by eliminating just one thing at the time.
But taking into consideration how milk and grains are often more than 50% of modern diet for a waste majority of people, very many achieve a great results just by eliminating these 2 groups.
Dets that are often free from those items are Paleo, Fodmaps, Grains free, low crab diets etc, very many videos on YouTube and generally a lot of info free available on the web.