The procedures for commencing a workers' compensation claim in the District of Columbia are found on the link below, and they apply to both insured and uninsured employers (there is a secondary public fund which is available to cover injured employees when the employer is not insured). Be careful when describing yourself as a "contract employee" so that you do not create the impression you are an independent contractor responsible for your own EC coverage. If you were paid by the hour and had no control over when and where or how you performed your duties (in other words, someone else instructed and supervised your work and told you what to do), then you are not an independent contractor and must be covered by WC insurance.
Here's the link: http://does.dc.gov/page/workers-compensation-does
Many employees hire an attorney to file these claims for them, but you can certainly start the process on your own.