I Don’t Have Medical Through My Auto Insurance

I was in a car accident (I hit a deer) as well as 4 other passengers in my car. I did have injuries to my knee due to the airbags deploying but I personally have medical insurance through my state that covered my trip to the ER. 2 out of the other 4 passengers went to the ER as well to be checked and they’re good, other than paying the expenses of their bill. Now my insurance doesn’t cover medical cost due to that not being apart of my policy. They asked for my insurance information so they can sue my insurance so their bill can be payed. As far as I’m aware they aren’t trying to sue me personally but I called insurance to see what I need to do in this situation and they told me they can’t sue because I didn’t have medical and there’s nothing to sue my insurance over and that it would be a direct sue to me personally and to give them my policy information anyways. So I did.. one of the passengers is lawyered up and assured them they can take a direct hit to sue my insurance over this. this was my first ever accident and first time being in a situation like this so i really don’t know how all of this works. Any advice ?