I would think to get a urine sample would be the way forward....now i know this can be easier said then done....yes i have chased round with a cup trying to get one!
The only thing i can say is perseverance...Then the vet can check to see whether there is a urine infection ect....
My tip?...BIG CUP FAST LEGS!..and good luck...
I will watch to see ,Archie's progress,I hope he is feeling better soon.