(Duplicating my answer to a duplicate question, which has since been closed)
You absolutely want to take computer science classes. There are development practices that you need to know about and terrible mistakes that you want to learn about in the classroom, rather than on a job. Despite how long you've been coding, you need to collaborate with professors and other students to learn the ropes. You can miss so much in entirely self-guided learning.
I'm in your same position, except about five years down the line. I had been programming since I was 12 and wanted web development to be my full-time, lifelong career. College classes helped me develop into a better programmer, but so too did the college community. From my first week in school, I started contacting community groups and businesses and starting high-profile community-based web development projects. Does your city's nightclub need an interactive online calendar? Does the art scene need an artist/musician directory? Maybe some annual community event doesn't have a website yet and you can whip up something interactive and useful. These are all amazing sources of experience, portfolio-building, networking, and fun. And I'd bet that any potential employers would rather see a list of practical-application community projects like that than only classroom projects. If nothing else, it helps communicate that you're driven and can work independently, which will immediately make you stand out from a majority of other candidates for a job.