The pH of human shampoos isn't right for dogs. Baby shampoo especially is very harsh and can dry their coat out. That might be the cause of her itching, although it could also be environmental/inhalant allergies which are more common than food allergies.
A groomer recommended Absolutely Natural shampoo to be years ago and that's all I use on Lady's face. I wash her face almost daily since she has dry eye and have never had any problems with it drying her coat.
Animal Friends Manufacturing Shampoo