Going to college with your major choices will teach you computer science, and you'll pick up some programming along the way. Conversely, going to work for a startup will teach you programming, and you may pick up some computer science along the way.
It depends upon what kind of programmer you want to be, and what you enjoy doing.
What I want to do (eventually) is start my own company that creates technology to aid education. I'd be lying if I said I didn't have a stack of ideas already lined up; however, I don't have the knowledge necessary or the capital. My end goal is to help people, and I feel as if it is time to decide the first real step.
If you want to be a developer of note without school, you're going to have to work your ass off, and then once all your ass is gone you're going to have to work up some ass debt and keep learning, except that you're not sure what to learn next, you don't even know what you don't know, you don't have friends in class going through the same thing or guidance from a professor. You'll be on your own. It will be stressful, and there won't be any pretty girls to kiss.
If you want to be a developer of note with school, then you'll have an incredibly solid foundation to build off of. And if you work on your ideas on the side (as you should) there's nothing better than learning something in a lecture and being able to go home and directly apply it that evening to your own work.
You've already said that you want to make technology to aid education, so immerse yourself in it. Get the best education you can, study the education you're getting, not just the material you're learning. Ask yourself, "How could this be better, how could I make some manner of technology to improve this experience, or bring this to other people?" By furthering your education, you'll not only be getting the tools you need to create your idea, you'll be doing the research too. It's always better to kill two birds with one stone.