Jazzie has allergies and the first sign of a flare-up is the itching. I notice it right away when I brush her. If it's not taken care of, her skin breaks out in red spots that later blisters. She also used to get yeast infection on her nail beds and in her ears. I know about the oily/greasy hair much too well.
If possible, get an allergy test. It definitely help me help her. I took Jazzie to a veterinary dermatologist and had her tested for allergies. I took the option of the blood test instead of the skin test and it helped to narrow things down. The test showed she is allergic to cats, dust mites and pollen as the top 3.
After lots of searching and talking to my alternative medicine vet. We switched her to Natural Balance Potato & Duck formula and it seems to be helping. I also use Earthbath Oatmeal and Aloe shampoo which has zero chemicals. I like the way it washes and rinses off.
From
www.dogtorj.tripod.com
"It has been known for years that the primary allergens in pets and people have been dairy (cow milk products) and wheat. According to the FDA, cow milk is the number one childhood allergen, followed in order by wheat, eggs, and soy. Eggs are actually a secondary allergen, meaning that we become allergic to them only after the intestine has been damaged by the first two early in childhood. This concept is explained in The Answer. The fourth most common allergen is soy. This is a primary allergen but has an interesting story behind it. Once again, The Answer goes into detail here, but suffice it to say that it would become number one if: one, we continue to eat it and do so in the quantity that is planned for us, and two, if it were as likely to elicit allergy antibodies as readily as the top two. Soy will be a "stealth" problem in that it is the least likely of the big three primary allergens to cause overt allergy symptoms."
There is a lot of detailed information on this site.
Hope you find a solution to help your baby.