For example, yes, seasonal allergies can be a problem, especially with lighter furred dogs. It can be pollen, or the grass they play on.
Or, it can be some food, such as corn. And, in your case, if he gets a nibble of corn from your food, his food can be corn-free but he can still react.
It can be your laundry detergent.
Is there a separate yeast issue, did they say, or do you think?
The indoor heat in fall/winter can dry skin, as you know.
And, this doesn't count an internal health issue, such as thyroid, etc.
So, what to treat?
I generally start with adding oil to their food. My best luck, when I was bringing abused dogs with bad skin and fur back to health, was a combination of cod liver oil and vitamin E. I've done olive oil, and others, but the cod and E got me consistently best results.
I got the E in a bottle, by the way, not soft capsules. It was more affordable.
Would it help the root cause? Maybe, but even in cases when it didn't, it improved their coat and skin anyway.
Does he get baths often? If so, you might need a different shampoo, and perhaps a conditioner.
Another thing that doesn't hurt, and may really help if he's been on antibiotics or has an additional yeast overgrowth, is yogurt.
I buy it plain, in fact, goat yogurt from a local ranch. The best way for me to have what I need, save money, and not waste any, is to buy a large container, and freeze it in portions, so that the last spoonful is as good as the first.
I know that many people give flavored yogurts, and you can certainly do that as well.
Note, if he does have a yeast overgrowth, sometimes it takes a round of systemic medication to clear them of it, followed by avoidance of yeasty foods such as breads, and also sugar. How are his ears?
I also put vitamin E oil directly on the skin, where there are spots that need help. I used to mix a dollop of cortisone cream, if using, with the E, and apply them as one.
Those are the easy things to try, which are good for him regardless if they help the root problem, or not.
I can't speak on Apoquel, except that Momo has had good luck with it.
Good luck, and please let us know what you try, and how Alfred is doing!
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