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!