My dog does not have seb. derm but she does have yeast due to her allergies and her dermatologist gave us Maleseb shampoo -- it also works on seborrheic dermatitis in dogs.
If you have not done so already, you might consider taking your dog to a board certified veterinary dermatologist as they are specialists in allergies/skin.
I would only use antibiotic cream on the dog if the skin is broken.
I bathe my yorkie with allergies once per week. I use the Maleseb when her skin is "scaly" and itchy. Otherwise, I use Biogroom puppy shampoo on her which is mild.
If you want a mild solution, you can bathe the dog as usual and finish her off by pouring a solution made with 1 part apple cider vinegar to 2 parts water. Pour over the coat (careful of the eyes) and then just let her dry. The smell will dissipate when the dog is dry. ACV can help with the itchies, I've found.
Good luck!
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