I've been hit by a zombie and started bleeding. I saw "Bleeding" in my inventory then I used a bandage. In the chat log I could see "You are no longer bleeding" and the indication in my inventory disappeared but I could still see the animation on my character and hear the moans.
I had to disconnect, then reconnect to fix it.

I have also experienced this twice yesterday and only after being hit by a player (I don't know if it's related)

It happened to me yesterday after being hit by someone (with a shovel)