Personally, I wouldn't relocate without a job. Though it's not impossible to get one, it can take a while, and $1500 will not get you far in DC (maybe a month or two). I understand being desperate to get out, but I'd still advise that you stay put for now, save money, and apply like crazy. As soon as you get an offer, head on out.
That said, if you really must do it, try looking at sublets or renting a room in a group house. Those would probably be the cheapest options in the area. Might not hurt to consider a part-time job just to help with the bills in the meantime. Depending on where you go, you might even get some health insurance out of the deal.