Other illustrators are self-taught because they learned best that way. Other illustrators have taken a middle road by taking specific classes but not working towards a degree. You need to decide what works best for you. Most illustrators end up learning new skills during their whole career. Very few schools offer courses in the business of illustration so you will have to teach yourself those skills on your own. It is a good idea to take basic business and accounting classes. One of the most valuable classes for illustrators is life drawing.
Whichever road you take you should also have a back-up or alternative career in mind. Very few illustrators can start out working full-time in any illustration field unless they happen upon a staff position, which are few and far between. You are going to need some other career or job to support you while you develop your career as an illustrator. Freelancing may never be a full time career or it can vary wildly from months of nothing to times of overlapping more-than-full time work. If you are young, then concerns like dental insurance and health insurance may seem inconsequential but they really are important. Some freelance illustrators have their second or part-time job in a creative field but other illustrators find that working in a non-art related field helps keep their creativity level high for their illustration work.