Shih tzus are very prone to a disease called keratoconjunctivitis sicca, or dry
eye. What happens is their eyes
stop producing their own tears, and the eyes dry
out and become very itchy and irritated. As a result, the skin around the eyes becomes red and inflamed looking, and it COULD have something to do with the redness and hair loss around the mouth as well, since these dogs have such short faces, the itchy eyes cause them to rub their faces on carpets, rough-textured furniture, etc.