Please don't wait another day to have him tested for Type 1 diabetes. If it's not that, then at least you've ruled it out right away. If it is diabetes, the doctor needs to start treating him right away. Either way, you'll know for sure.
If it's not diabetes, be persistent in asking the doctor if any other medical conditions could cause such sudden, excessive thirst. The intense screaming when you refuse could be either due to real thirst or pure control issues -- it's almost impossible to tell with a child this age who can't really express himself yet. But ruling out something medical, especially with such a sudden onset, is essential. If you call today, I bet the doctor will want to see him ASAP.