Not sure about Barnard, but there are colleges that do allow an appeal process. While a rejection is hard, hopefully something will stand out in your application and you will find the place you’re meant to be, if not Barnard. It may not seem like it now, but there are thousands of colleges out there and there is a great one waiting for you. If you end up somewher else and truly feel Barnard is for you, then you can always try again at a later date to transfer, but don’t close the door on other schools. Things usually do work out for the best.