If I had a choice between an art museum and an aquarium, I would choose the aquarium. You do not have to be an artist to become a designer. Right now, you do not have to have a college degree. A technical degree would be helpful because you need to know lots of software such as Adobe Photoshop and Quark Express. The best plan is to try to get an internship.
Web design means learning to use many different types of software.
This is a wonderful career. You must constantly learn and grow. If you want to have a job that is always the same, this is not the career for you. I read technical magazines and learn new software every evening. You will spend a lot of time learning on your own.