First of all: yes - there is no reason why your degree should prevent you from becoming a business analyst in the future. Also - there is not need for you pursue another college degree. You could always decide to pursue a masters degree at a later time.
The reality though is that you don't have any experience nor education in business analysis. Therefore, I would suggest that you get started but investing in a good introductory course in business analysis (ideally instructor lead). This will help you not only gain a good understanding of the profession but will also provide you with the opportunity to discuss more details with the instructor and fellow students.
Best of luck in your future endeavors!
Adrian