Traffic Accidents: No Insurance, but Not at Fault, Am I Liable 100% for Other Insurance Claim

I was involved in an accident that was caused by a traffic sign that blew onto the highway. I was not cited for being at fault, but I did not have insurance at the time of the accident. I hit the car in the lane next to me which caused damage and her insurance is now coming at me for the whole amount of the accident. Am I liable for the full amount or do I have any rights? I feel that I am partially responsible but feel 100% is unreasonable.

Traffic Accidents: No Insurance, but Not at Fault, Am I Liable 100% for Other Insurance Claim