As long as you're infected even a tiny bit, your health constantly decreases. If you're very sleepy or hungry, it decreases even more, so make sure you sleep and eat. Immunity has no effect on the decreasing health, it just prevents you from getting *more* infected.
There is no way to know if you're "bleeding", as far as I know. It's just the game's way of telling you to use bandages if you get wounded. (Ironically, you can survive starvation through bandages as well, but we'll forgive an otherwise difficult game for being so generous
)