Is it worth to study culinary arts when running your own restaurant???
What's the rush? You haven't graduated high school yet. You have not said that you have any experience. Once you graduate, find a successful local, independent restaurant and talk to the owner. Work in the kitchen. See what the business is like. Visit a different restaurant. Visit three or four or a dozen. Find out what you are getting into. Culinary school is not cheap. The restaurant business is extremely difficult. Both require massive amounts of hard work and discipline. Do some research.
Before you invest any time or money into further schooling, I would strongly suggest working in a restaurant for at least 6 months if not a year or more. See if you actually like it first before investing too much of yourself down a path you might hate. Its very hard work no matter what, but some people love it and some people hate it, and you won't know which you are till you actually do it. And if you don't absolutely love it, don't even try to own a restaurant unless you are independently wealthy and can afford to lose a few hundred thousand dollars.