I'm sure you're aware but there are hereditary breathing problems in the breed:
Stenotic Nares - Stenotic Nares is a condition where the narrow resticted nostril puts a strain on the dog's system and can lead to an enlargement of the heart. When the surgery is performed the veterinarian removes a portion of the nasal cartilage to enlarge the nasal openings. In this disorder, the openings to the nostrils are too small and the puppy has a really hard time breathing through the nose. Stenotic nares is an inherited defect. An early surgical intervention can provide adequate airway flow that helps prevent the development of secondary problems like tracheal collapse and chronic bronchitis.
General Respiratory Problems - Shih Tzu have a lot of respiratory problems related to the shape of their face and head (the brachycephalic syndrome) which affects mostly dogs with a short nose (brachycephalic breeds). Due to an obstruction in the upper airways, the dog is forced to labored breathing. Not every brachycephalic dog will develop respiratory problems but most will to some degree or the other. Severe problems may require surgery.
Talk to a knowledgable veterinarian to see if the continued sneezing may symptomatic with an inherent problem. If not, it may be allergies, also something to test for.