As far as I know, there is no reason whatsoever that you can't have a cold drink or wash your hair during your period. Those sound like old-fashioned superstitions with nothing to back them up. With all due respect to your mother, I would suggest that you and she go to the library and check out a book on the female reproductive system. I'm sure you won't find anything scientific about those "old wive's tales" in a book written by medical experts, and perhaps that will calm your mother's fears and clear up any misconceptions she may have. Good luck!