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To become a car designer (especially if you want to design the look of the car), you may want to look into various art (industrial design) or architecture programs. Another option would be to look into Engineering (Mechanical and Electrical Engineering are the most directly applicable).
As far as which colleges can you attend, there are far too many factors to completely cover here, but here are some highlights to consider when choosing a college:
1) Find a college you can afford. I don't know what your situation is, but this will be key.
2) Make sure it is not a for-profit college (private non-profit is fine, but avoid for-profit schools). Degrees from for-profit schools are generally thought to have questionable quality (whether or not they actually do).
3) You already seem good on this one, but pick a career and then plan out your college career to get you to that goal. Also consider what else you might be able to do with your degree since life sometimes throws you curve balls.