There has been a lot of excellent advice posted... I will add mine
A.)
Food-- the corn may be the problem. I also use the natural balance limited ingredient.
If my babies spend the night at a friend who uses "regular" food they come back itching!! - Also ear infections stopped when I changed food.
B.)
I just added salmon oil - I got it at petsupermarket. I see someone gave you a link to purchase online. Before that I used fishoil tablets that I cut opened --weee my finger did smell ;(
C.)
At this point you have to worry about staph infections.. please see the vet.
Also -- when this started with mine I had to get shots a few times to "get over the hump" so to speak.. to give the little guy some relief
D.)
Flea bits can cause allergies - that is what I had to get the shots for.
F.)
Check into apple cider vinegar -- there are some post on yt that were so good I purchased it and started yesterday.. add to drinking water and add to rinse water
G.)
I use t-gel (tar) shampoo and it helps
I am sure I repeated a lot.... but if I added anything that helps you I am gald. I have a shih tuz and Laso that have major troubles with skin and have tried just about everything over the last 6 years...above is what I have learned that helps