Employment Outlook for applicant with BS in business and Ass. in Java soft. dev

I had a meeting with my school advisory (I posses a Bachelor's in Business and am working toward associates in Java software development), she told me if I wanted to stick with the Bachelor's I have and get the associates (as apposed getting second BS in Comp Sci.), I was likely looking at a career in client side programming (not so much server side). My understanding of it so far is that it deals with the user interface aspect on a browser, also, she mentioned possible stand alone business applications. I would be working with a team of programmers in putting together one big code (I have learned that she was referring to "code monkey" work). So it's clear that this path is aimed at programming: simply coding the desired tasks by the "developers", not the "Software developer" job that is so lauded by business and computer magazines.

My question is, does this lack of a BS in comp sci permanently limit my career outlook to programmer? Or could enough creativity and determination open the doors for the "Software development" opportunities that go beyond the "programmer" title?