After visiting the litter box three times in fifteen minutes this morning, Whitey won himself a visit to the vet. Mew! Without his brother. Mew! The verdict is a possible bladder infection, calling for a course of amoxicillin. Fun fun fun.
The good news is that these things are apparently not very contagious, so Billy is unlikely to get it.
He apparently wasn't too traumatized, though. He is now napping in his carrier.