You're 19. You're not "running away from home." You're leaving home to pursue your own interests and passions, and with $13,000 you absolutely can.

First thing you'll want to do is acquire housing, so I'd figure out where you want to go to school and move there. Use some of your $13k to get temporary housing while you find a job so that you have income and can then get a lease of your own (or look around for people looking for roommates if you're comfortable with that. )

Once you're set up with a job and a place to live, it's just go to work, go to school when you're ready and live your life as you please in between.