Feel your pain. Same thing happened to me a couple of years ago. Stopped on the freeway in rush hour traffic and a girl in a Dodge Durango smashed into me. Rear quarter panel, bumper, lights, trunk gone. Damage came to around $10,000. The rails were not damaged, so my dealer's shop replaced everything. The claim can be handled two ways. Either your insurance pays and goes after the other parties company or you deal directly with the other insurance company. The advanatge of going first through yours is repairs can start right away. You would pay the deductible (waived in your case) and get it back from the other company. If you decide to deal strictly with the other company, be prepared to wait for repairs to start. Also, question what parts will be used for the repairs. Most insurance companies require the body shop to first go out and see if less expensive "used parts" are available. Most come from junk yards. I was lucky and got all new parts.
The good news is it's amazing what a good body shop can do now with repairs. Mine came back with no indication from the surface that the car was repaired. Paint matched (black shapphire), panels lined up, even the weld seams looked new. After a month driving a Prius, it felt great getting back into my car again.
One kicker after everything was finished. My premium from State Farm went up a little on the next renewal. I questioned it and my agent said SF had a policy they would raise the rate even if I was not at fault just because I was involved in a claim related accident. It was a small amount, but I hit the roof. My agent got around it by swapping the policy on the BMW with the policy I have on an old sports car,resulting in an "accident free" policy for the 535. Crazy.