Wow I think the Uni is really out of line - telling you to get counselling so you can manage yourself when people actively discriminate against you - WTF! Talk about institutionalising bigotry!
I know this is the last thing you probably have the energy for OP but really what's happening here with you is awful. Please write a formal complaint to the hospital citing dates/times/quotes of what you have experienced with specific names. I hate to think that people like this get away with such revolting behaviour.
Good luck for the new placement! I'm glad you will get to finish this year! I think it's terribly sad that you feel you need to get speech lessons to change your accent