After a work injury, you may need immediate treatment, whether you go to the hospital or a clinic or a private doctor. But how do you pay for that medical treatment you need?
In D.C. the workers compensation insurance should pay for all of your medical treatment related to the work injury (and remember, in D.C. and Maryland, you choose your own doctor - don't let the insurance company make this choice for you).
But they may not have a claim set up before you need the medical treatment, especially in an emergency. It's OK to use your health insurance initially, and they can be reimbursed by the workers comp insurance company (and you can be reimbursed for any co-pays).
After that, you shouldn't use your health insurance or pay out of pocket for medical bills - that's the responsibility of the workers comp insurance company.
If they deny your workers comp claim or don't authorize the treatment you need for your injury, then you can use your health insurance or pay directly. Keep all of your receipts so you can get reimbursed if you win that issue.