What degree do I need to switch to a Graphic / Web Design career?

To be completely honest with you, your degree doesn't matter in the long run whether it's an AA or BA. Ultimately, what gets you the job is your portfolio. If you know what you're doing and make the most of whatever program you decide to enroll in, your work will be enough to attract potential employers. I've seen amazing self taught designers with only a high school diploma and I've seen complete amateur garbage from BA graduates. Don't focus on that piece of paper, focus on getting good. Really good. It's an extremely competitive career path and you have to put in everything you have at this stage to distinguish yourself from the average.