I don't understand the way the vet is getting a urine sample. I've been told for a urinalysis what really needs to be done is the vet takes a sample directly from the bladder with a needle? That's how my vet would test Max's urine (this is when they do the urinalysis at the vets or send out to a lab). With an experienced vet–it isn't painful. Also--if Max had just gone potty--and his bladder was empty--they would sometimes have to confine him there at the vets in a kennel and wait for his bladder to fill up before taking any with a needle. This might take a a couple of hours to get a good sample.
That also struck me as odd that the vet didn't draw direct. It sounds very serious I know how you feel. I hope he gets better soon!