I get eczema, acne, and other skin conditions when I eat too much carbohydrate. If my experience is any guide, it may take a year or two for the eczema to fully be resolved, but you will most likely start noticing an improvement over the next month or two.
I used to get eczema on the backs of my hands every autumn until late spring, and while I noticed an immediate and ongoing improvement after going keto four and a half years ago, it was only last winter that I didn’t get any at all. I recently overate some carbohydrate a couple of weeks ago (I am not on a carnivore diet, though perhaps I should be), and suddenly it started up again in the usual spot. I’ve made a real point of cutting carbohydrate again, and it finally went away a few days ago. Normally in years past, only cortisone ointment was sufficient to keep it somewhat in check.
Give it time. My skin has improved immensely by eating carnivore but it took months. I noticed the first few weeks that I had really swollen joints, gastrointestinal issues, and skin flare ups. But those went away as my body flushed it out, and I bounced back immensely over the last couple of years of carnivore.
One big key, is just eating fresh meat, no cured stuff like bacon or ham or slami, or canned stuff like tuna or salmon, as you start carnivore.
I also noticed that foods high in histamine made it flare up initially. I had to avoid lamb, especially when it was shipped from overseas, pork, or even beef that wasn’t super fresh from the store. I tried to buy in bulk, but after the meat sat in my fridge for a few days, it seems to cause flare ups when I ate it. Now, after a couple of years carnivore, I can eat pork or bacon, or canned fish occasionally without any skin, gut, or inflammation flare ups.
Have a look at this article, it may help explain a lot