Originally Posted by: hunter1801I graduated a couple years ago with a degree in business. I have been self employed since 2010 as a "musician/graphic designer".[/quote]
Make sure to show a clear connection between those two. You have a business degree & you are, in essence, running your own business.

To that end, you should consider obtaining an official small business license. If you already have one, good for you. Use that on your applications: "Hunter1801 Company, small business, sole proprietor, since (date)". You can describe the work you do if necessary or desireable: "Manage band marketing, promotion, booking and branding" as well as, I assume, performing.

If you haven't already got a license, get one. You can still put it on your resume. If someone asks about the discrepancy between the company official start date & your time working it, you can honestly tell them that you started doing it, then at a certain point you made it successful enough to require making it official.

Prospective employers with a clue will know that doing anything yourself & earning money doing so, requires seriousness of purpose, ambition & discipline.
[QUOTE=hunter1801]The jobs I'll be applying for wouldn't necessarily be related to music, so I don't know how I should handle it.

I don't know what those jobs are, so I can't say exactly how, but you should find general skill sets & activities you do in your band biz that parallel the skill set required in the job for which you are applying.

Hope that helps. Best of success!