Have an Answer?
Education is always the best investment. I'd recommend you get a bachelor degree. But, please be clear with what you want do exactly, most web designers nowadays know web development too, with what they know on the development side, they apply it into web design, layout, and user experience, come up with good modern web design, which has a tons logic behind it, for marketing, business development, SEO, etc purposes.
This may sound complex than you think, but it's not. Once you get a job, you will be asked varieties of design and user experience insights. That's where you can grow too.
You probably need to look some digital media/multi media majors. Which these classes should teach you the arts, drawing, painting and software tool skills like photoshop, illustrators and indesign etc.
Web designer is a fun job if you like to design things with results on devices(computer, tablets and phones). Art design is totally another story.
I found that most jobs require a bachelor degree in IT field. So if at all possible, i would advise you to do a 4 year degree.