Kinda late to the discussion, but we have a Zuchon, which is a cross between a Shih-Tzu and the Bichon. The little dog (primarily Mrs.
C's) is a lot more Bichon than Shih-Tzu or so it seems to me.
She's also experienced some skin rash, Just as
Jan1957 says, it does seem to be part of the breed, especially the pink skinned ones. But, after visiting with our trusted vet (we're in the U.S., by the way) and doing due diligence I arrived at the solution being almost entirely diet related.
First, we got rid of the bagged, supposedly high quality dry dog food and replaced it with a raw diet. We use only raw beef, lamb or fish with occasional organ food (kidneys, heart or liver). We also use cooked bones (beef) as well as some semi-cooked vegetables.
Next, remembering my Dad's dogs and his health remedies for them, we used some Vitamin E, C, Brewer's yeast and Fish oils with Omega 3 and 6. fatty acids. Additionally probiotic, which can be purchsed at health food stores or simply feeding some yougurt each day, which she loves (unflavored is best).
Finally, on a hunch we also began giving bottled spring water...quite cheap at the grocery store, instead of tap water whcih in our home is softened.
I realize this seems work intensive, but it really isn't andthe results have been a complete elimination of any itching or rash. She's a much happier little dog. It even contributed to house training, which is difficlut with this breed.
At any rate, here's a good source for information:
http://www.bichonhealth.org/
Good luck!