Tiny red spots back of 3 yr old throat, tummy pain, high fever, no appetite. Doc says hand foot mouth. But what else could it be and can I look out 4?

Strep throat. Strep usually causes abdominal pain; but if he had a strep test and it is negative, likely the doctor is right and it could be hand-foot-mouth. Feed soft lukewarm foods and plenty of room temp liquids, nothing scratchy, acid or carbonated and use Acetaminophen for discomfort--should be better in a few days. It is possible to have both.
Other considerations. I agree that your child may have Strep, another viral infection or a possible pulmonary infection which can cause abdominal pain and fever. If the symptoms do not improve or if they persist, I would advise a follow up visit. Your physician may obtain a throat culture for Strep. Hand, Foot and Mouth disease is a viral illness which improves with time and usually resolves by the 10 th day.