A few questions to consider, does your budget take into consideration condo fees? Have you actually been approved by a lender.
Locating a home, analyzing the total monthly cost, and locating a lender are all things a good realtor can help you with. If you have any additional questions, please feel free to contact me.
That is a little tight to buy a property in DC. Currently under $200k on the market in DC in such neighborhoods at Adams Morgan, Chevy Chase, Brightwood, Logan, Cleveland park and others there are studios. A 1BR at that price point is going to be tough in DC. Please feel free to email more details and I would be happy to send over what is on the market and help you find a place to buy.