As a groomer and having a Shih Tzu myself, most of this breed have allergies and usually start at the base of tail, You need to try bathing her in and oatmeal shampoo also use a conditioner. You also don't need to bathe her anymore then once every 2 weeks it drys the skin if done more than than, also try to get a higher grade of food make sure the first ingredient is a meat. If it does not go away or get better talk to your vet about an allergy peel or shot.
Seems to be a common problem all this itching,scratching, dry skin,biting base of tail ( probably the only part of its itchy body it can reach) fur coming out due to the biting. We had the same problem with our 8week old pup. Changed its diet to higher meat content, instant success, 1 week later the fur had grown back,no more flaky dry skin, biting tail. We tried change of diet first and was successful, this may not always be the answer.Pet shop assistant spent £3,000 on vet fees first, before changing diet to food with higher meat content ( his was a shih tzu). Our adult dog has also benefited from this, his teeth are cleaner,coat thicker,less moulting,appears leaner. Dogs are carnivorous.