I would watch him-consider taking him to see a veterinarian, especially if he continues vomiting, has diarrhea,is lethargic, not keeping food and/ or water down.

Have you fed your shih-tzu anything different? Sometimes a change in diet, even treats, can cause an upset stomach. If the dog  vomits a lot and doesn't want to drink or eat,or is lethargic,you may want to seek veterinary care.

This sounds potentially serious and you need to seek veterinary help right away. Is this a male cat-he could have a urinary blockage and can die if not helped.