4 year old in school, coughing, red spots on soft pallet roof of mouth, says mouth hurts, runny nose (spots are not blisters). Causes?

Most likely viral. Could be hand foot and mouth disease (if there are bumps on foot and hands) - which is a virus, or can be cused by other visrues or if he has a sore throat it can be strep.
Red spots palate. This sounds like strep throat or another type of viral infection. See your pediatrician to have this tested.