I agree you need to go to the vet on Thursday with the early morning sample. You may be told it's too dilute to test when they drink too much. To know how much he's drinking, fill measuring jugs or a fizzy drink bottle with a quota , then tip the leftovers back in so that you calculate how much was drunk. The vet may mention diabetes insipidus, but this is often a symptom of something else, and doesn't require drugs. Diabetes mellitis is the one needing insulin. Is he eating and pooping normally? I would hope for a general blood test, urine test and thermometer reading. I would also crawl out of bed in the night to let him out before he bursts, he must be uncomfortable attempting to hang on.
My springer suffered with this before she was diagnosed with a pancreatic autoimmune disorder but she had the runs as well.
I hope it's something simple like a UTI, Wish you well for the appointment. If you're worried, do go sooner.