The short answer is you won't necessarily need a degree to become a professional sound designer. However, it certainly helps if you at least have some experience in music or multimedia production. While most companies are looking for individuals with degrees, many projects can be handled by freelancers who are good at what they do and may not have the time or resources to find someone else. However, continuing your education through courses related specifically to sound design will definitely help you stay ahead of the competition within this highly competitive industry. You may also want to consider taking courses that teach digital editing or multimedia programing skills so you can offer more services to clients in the future.