Here are Shih Tzu common skin problems and helpful grooming tips to keep our furry babies healthy and adorable. Shih Tzus can sometimes suffer from food allergies along with allergies to other environmental elements such as pollen. Signs of allergy resemble those of other skin diseases, such as constant scratching, hair loss and lesions. Check out this quick video and it may help finding out if it’s a common skin issue or if you might need professional help.