For a while my kota kept having dry skin problems. Our vet put her on a supplement for a little while (omega i think), and it helped some. However I found this shampoo and conditioner we love and it has done wonders for dakota's skin and coat. It is called Wags. It is a natural wheatgrass shampoo and conditioner made for dogs. It has oatmeal, aloe vera, vitamin e, papaya, kiwi, raspberry, and mango extracts, chamomile, and wheatgrass (of course. that is just most of the ingredients off the back). Once we started using it dakota's coat started looking much healthier, and now she doesn't have any dry skin issues. I am not sure if you do this, but I ALWAYS use conditioner on her after shampooing. And with Wags, I can scrub her down, use the conditioner, rinse, towel her off, and still run a comb through her hair with no tangles!! It is amazing!
Hope this helps, and hope your little one gets better soon!
tamara and dakota