Somebody's insurance should pay. If you have not already done so, assuming that you have a homeowner's or renter's insurance policy yourself, you should immediately notify your insurance company of the event. Today.
If you get to the point where the two insurance companies are fighting with each other over which one of them should pay you can rest fairly securely that you will get paid for your losses. They will come to a compromise "over your head" and you should not really be required to do anything else. This is why you have paid for the insurance after all. Make them do the work for a change.