I am currently a b school student Anderson '14, with some relevant experience.
If I read correctly you currently have a bachelors degree? If not make sure you get that taken care of- additionally, try to contribute to papers and blogs as much as possible.
Two things:
1: Your choice of major for undergraduate degree will not hold you back from getting accepted into quality programs, but a lack of analytical skills definitely will hold you back.
2. A master program in writing through a school with a strong network (USC etc.) could prove to be paramount to you landing the type of job that you want.
Also remember that sports writing has shifted to greater appreciation for data analytics. If you can carve out a niche with your local papers as someone that really understands analytics you can likely make a case for yourself to continue to climb up the sports journalist ladder.