Go to the nearest welfare hospital and get seen then, and let the insurance paperwork catch up.
It took me two weeks to get there with my hand. In hindsight, I should have just gone to the cook county hospital first and got treated. I ended up doing that two weeks later... The emergency room had a 2 hour wait the day I went, but the hand specialist I see there has not had me wait more that 40 minutes after checking in.