Guaranteed Healthcare

Riding my bicycle home from work after a night shift, I crashed after someone opened their door from a parked car. My bike and I were a bit banged up, but I didn't make a big deal of it. I took care of the bike myself and figured I'd heal OK. She was a college student and I figured she didn't need the headache for a simple mistake. Well, two weeks later, I still had a large bulge on the side of my calf and a couple of reasons to be concerned it may be getting infected so I went to the ER after work (hospital employees can use as an urgent care). I'm still waiting to see how things turn out with the antibiotics. What has me bothered is that because the injury involved a car the hospital is saying that they have to send the claim to my auto insurance company because my health insurance would deny coverage for an event involving car. I now have to "correct" the scenario of the injury because I fear that because I didn't get that girl's insurance info, my auto insurance company will deny payment. And if my health insurance won't cover it, I'm the one to get stuck!