Just went through this myself. The auto insurance wants to wait until all treatment is complete before they pay out on anything. I'm sure they want to just cut a single check and then have you sign something to release them from further liability. It stinks because that puts the burden on you to handle the expenses until they pay you back.
I tried to give them the info on my medical insurance so they could pay them back for my medical expenses. But, they told me they wanted to deal with just me and it was up to me to reimburse my medical insurance company. I contacted my medical insurance company anyway -- partly to be sure they would still cover my expenses and partly to give them the opportunity to deal directly with the auto insurance co. They are in communication with the auto insurance company but told me it is pretty common for them to just deal with the injured person and leave it up to you to reimburse anyone else. It's still a very good idea to keep the medical insurance company in the loop.
I recently had my final doctor's appt and submitted the paperwork to the auto insurance company this week. We'll see how it goes with getting a settlement and closing things out with my medical insurance.
I hope your healing goes well and you feel better soon.
2004 Colnago Chic - WTB Deva
2008 Blue RC7 - WTB Deva
2009 Colnago Master X-lite - WTB Deva