I think he has rabies, but not from dogs. I'm guessing bats.
So, in this chapter we learn that Michizane's elder brother contracted a disease with similar symptoms as Kajimaru, and this prompted Koreyoshi (Michizane's father) to avoid dogs even as he continued to keep hunting falcons. Possibly his first son contracted rabies after being bitten by a dog. Kajimaru probably caught it from being bitten by a bat while skulking around ancient Jin tombs.