We have a two year old Zuchon (Shih Tzu/Bichon cross) that should be similar in coat quality. She's had skin irritability off and on but we have her trimmed about once a month. When she has started scratching, especially in just one location we, on the advice of our Vet, (he has a really nice boat, probably at our expense) use any over the counter lotion containing either Colloidal Otameal or Green Tea Extract... I'll say it works very well within just a few days.
If it continues, you may wish to have her tested for thyroid problems, however...