More important than a degree is a porfolio, preferably a portfolio of production work (versus classroom work or goof off work... unless your shit is really really good).
I do a lot of graphic design work (as well as some grapic arts), and my number 1 suggestion is that you broaden your scope of interest into digital design, encompassing both print media as well as web stuff. If you can finda school that will give you some introductory-to-advanced courses in some of the main software packages, get enrolled. When you're not in class or working on an assignment, create multiple projects for yourself and learn how to work quickly. The main problem (as I've observed) with design graduates is that they work very slow until they've been in the business for a couple of years.
In the meantime, learn the difference between vector and raster, learn the difference between RGB and CMYK (as well as what they are and when you need them), learn the difference between setting up a job for silk screening versus heat transfers, and get aquanted with the following programs:
Adobe Photoshop
Adobe Illustrator
Quark Xpress
Adobe Acrobat
Some other programs that will help you a great deal (and diversify your skill set) are:
Flash
Image Ready
Fireworks
Adobe InDesign
While you're at it, do some research on color theory, and get aquanted with some formal rules of design (composition, composition, composition).
Also, learn why you'd export at 72 dpi versus 150, versus 300. And Pantones. Learn about Pantones.