Birds don't usually get diabetes, and unfortunately renal or kidney disease is more common. If you're noticing this, this is pretty severe. I'd definitely recommend finding an avian vet to do blood work as soon as possible!
Hi,
Budgies can get many illnesses which look similar and may include increased thirst and urination. Do see an avian veterinarian and bring the cage with unlceaned bottom paper so the doctor can see what has been happening.
There are many veterinarians in the Boston area, and one option is Angell Memorial AH in Jamaica Plain. They will have a doctor who will be able to diagnose and treat your bird.
Good luck!
Sincerely,
Arnold L. Goldman DVM, MS
MedHelp & PDOC