Hi there, I had something similar sounding about 5 years ago (and it had been going on for a good 4-5 years, nothing I tried worked - naturopath, dermatologist etc.) - then in 2016 a dermatologist told me I had a severe reaction to the skin care products I was using (dermatitis). I had to ditch them for the most basic cleansing routine - and haven't looked back since.
Unfortunately this dermatologist was one I see in South Africa so I can't recommend you see her - but if you can find a similar product to the one I got in SA it would be worth trying it out.
It's called an emulsifying ointment (or dry skin emollient), and I used it for both washing my face and as my moisturiser.
The one I use has this ingredient list: "Ingredients: Petrolatum, Paraffinum Liquidium, Cetearyl Alcohol, Ceteareth-20. " and the label says "contains Cetomacrogol" so that would be someting to look out for as well.
It sounds quite hectic, containing paraffin etc. (and so many people will tell you not to use anything mineral on your skin) but I am living proof that it works!
Good luck!! x