My eldest DS was always like this!!! Everyone would tell me to have him tested for diabetes, in the end, I caved in and got him tested. No diabetes, just a thirsty little guy! He is now 14 and still exactly the same. He takes a 2lt bottle of water to bed with him at night and drinks the lot throughout the night. All up he would drink around 4lts a day now. I just make sure he has enough salt in his diet too (we use celtic sea salt) because all that water can strip essential salts and minerals from your system.
I hope your little guy is fine. What a PITA having to wait so long to see a Dr. I hope next time you go, someone cancels and you get in quicker