In the design world a degree simply adds a rubber green stamp of approval, the quality of your work should speak for itself.
However, that being said, in the professional world a degree is a virtual must, companies like to tell their clients that their team is well qualified because so and so attended such and such a school, therefore they must be fantastic.
Getting a degree means you will also have spent time in front of formal critics, which will help you to develop not only your style, but also your ability to communicate your thoughts, your presentation skills and your ability to work with others... if you want to work for a company, they are going to want to see all of this.
Personally, I would and have hired designers without degrees, but if you're looking for work in the larger company you may have some problems.
If you are not thrilled about the idea of going and getting a graduate degree, I might suggest enrolling in some university courses and working towards a design certificate or something to that effect.