Wow, what an unlucky accident. It doesn't suprise me that the ER doctors missed that, often when I have had an ear infection (and go to the clinic) they look in the ear, see it's red, then say "you've got a cold it will go away on its own". Then I come back in a week in severe pain with discharge and they say, OK, you've sufferred enough, now you get antibiotics. Why should I suffer at all?
Anyway, hope you feel better. I'd refuse to pay the ER bill if I were you. They should consider themselves lucky they didnt get sued.