I'm so sorry this has happened to you. I'm Muslim too and had placements while at Uni (teaching) and had to deal with some of what you've described, particularly the obsession with "where are you from". It's so disheartening and upsetting!
I have no other advice for you, I think there's been some excellent suggestions in this thread. Please take the advice you've been given and go above your coordinator's head; your university has absolutely failed you on this and it's outrageous.
Also I would name and shame the hospital and department. This woman has acted disgustingly and it seems the rest of the department are no better; as a Muslim I would hate to be a patient there, I can only imagine how I'd be treated.