My vet suggested changing dog food to a natural blend food. He also stated that if the dog food has any color besides brown, it has additives and it is not good for your dog. Sharda has been speaking about using natural blend dog foods - all of that totally agrees with my vet. It seems like the red skin for a Bichon is pretty common though. Many that I've seen have pinkish skin, including Phoenix.
That does sound like something to check with your vet about. Of course, it never hurts to feed your dog a very natural dog food. No vet would ever say that is a good idea. My vet told me that if you don't understand what the ingredients are, they are not natural ingredients.