Neighbors Tree Fell On My Car And Garage.

Last Wednesday while I was out and about, I received a call from my brother that a tree was on top of my car and garage. I came home to find a tree from my neighbors backyard had fallen into my property on top of my garage (not sure of all the damages on the roof of the garage but it did bent my gutters)and on one of my vehicles causing some minor scratches and major dents on top of the vehicle, while completely breaking off a side mirror from the passanger side on another vehicle. It happened around 11pm so i deicided to go over the next morning to grab her insurance information to file a claim. She kept dodging me and my calls until yesterday which is 4 days after the incident and i finally managed to grab her insurance info. I called her insurance this morning and they said she has to be the one to file a claim, and that they are not responsible for her tree damaging my property and i have to call my own insurance and make a claim through them. The vehicle with the dents and scratches is recently purchased and i had not even had it registered yet. I also do not want to go through my insurance and bump up my rates. What are my options here that does not just end up with my being responsible for any of the financial burdens. Can i file a claim against her insurance? Do i sue? Please help! Thank you in advance for the answers!