Is 3 teaspoons of 250 mg amoxicillin to much for a 3 year old?

Depends on the mg/ml. My drug book says mild to moderate infections is 25 mg/kg of weight per day, for moderate to severe 40mg/kg. If a medical professional hasn't given you the prescription for the 3 year old you should not give it. All medications for kids this age can result in adverse reactions that are sometimes life altering.