Put simply, absolutely not.
Most of my employers have never asked where I went to school, and quite a few of the designers I've worked with never attended a design/art college. Having a degree is a great thing, and by no means is it necessary.
There are countless resources online which can help you learn the tools of the trade. Much like anything else, you must first learn the basics. I would suggest finding books on amazon or at your local library on graphic design. From there I recommend starting to learn photoshop, one of the most versatile tools a designer can use. Tuts+, Lynda.com, photoshoptutorials.ws, are all great places to learn how to use photoshop.
In the meantime, continue learning about design as an art, color theory, typography, iconography, interface design, desktop publishing, branding, product development, etc. After you're comfortable with photoshop, there are several other adobe products I would consider learning.
If you manage to find a curriculum for a school you wish to attend, perhaps start searching for online tutorials related to those courses, and start learning now to get a jump start on your path to an amazing career.
Best of luck to you!