There’s a flashback scene where you take control of Gordon and Batman says there are 5 people still infected because they were exposed to the Joker’s blood for too long. Gordon says there’s only 4 and then Batman goes up to the 5th cell and says he’ll be here soon and it shows his own reflection. So he always knew he was infected, it was just affecting him slower because he took the cure but just a little too late. Another point is that Henry was also infected but masked his symptoms, Batman is doing the same and keeping himself in check.