My parents's Yorkie female, Penny, who I grew up with had severe skin issues. She is 10 years old now and you would never know she had trouble with her skin. She would itch and lick constantly. Her skin was dry, red and swollen. It would keep her up at night.
The first solution we tried that gave us good results was adding a
probiotic powder to her food. The product claimed that dogs without the proper balance of flora in their gut can have coat issues. It worked pretty well, but it wasn't a perfect solution.
We have drastically improved the quality of her
diet. This has been a major key in her improvement. Remove wheat and corn from your dogs diet. Rice and quinoa are okay. My parents are currently making her food out of cooked quinoa (cooked with a vitamin, an egg, etc), raw BUBBA burger, and B.A.R.F. (Bones And Raw Food). It may take a month or two for you to see some improvement, but stick to it. By six months you will see many improvements in her coat, energy, and temperament.
The third thing is the
shampoo you use. Oddly enough, I also have very sensitive skin and skin allergies. I struggled for years with the same symptoms as Penny on my scalp. I finally found that mainly the lauryl sulfate and lauryl sulfite (and some other ingredients) found in most shampoos were the culprit. Many people, even those who do not have symptoms from using normal shampoo, experience amazing results after switching to a shampoo that does not contain these ingredients.
Now I use
Wen Cleansing Conditioner on myself and all of our family's dogs. It is expensive. But, it is the only product that I use. I no longer use hair sprays, gels, mousses, etc. I also save money on pain pills, allergy pills, cortizone, and dermatology visits. The same cost benefits will apply to your puppy.
Wen has drastically changed my life and Penny's. Now I have gorgeous hair that everyone compliments. Penny also receives compliments all the time. She loves hearing people say "You're so pretty!" and she knows what it means. Now she only itches if she needs a bath or if she's been rolling around outside in something gross (especially during allergy season). Her old symptoms have never returned.
Wen is safe to use on children, dogs, and adults. The creator of the cleansing conditioner, Chaz Dean, uses it on his Labradors. I have found the best results using the Tea Tree Cleansing Conditioner so that is the formula I recommend. Here are links to Wen and B.A.R.F.
Chaz Dean Studio BARF Diet - Healthy & Natural Raw Food For Dogs & Cats, Pet Health Care Food & Nutrition Products Supply Online