vehicle accident

hi! i was involved in a car accident last year involving 3 vehicles. the vehicle in front of me hit sudden brake and because it was raining, i was not able to entirely avoid hitting it. i hit the vehicle in the corner rear bumper, my headlight was damaged but the vehicle only had scratches. apparently it hit another vehicle in front of it which has damaged rear. i was then told that it was my fault because i was the third vehicle! all the officer explained why im at fault "ganun talaga kasi nasa huli kayo". is that how you analyze a vehicular accident??? "ganun talaga"?? i explained that my impact cannot cause the vehicle in front of me to bump on the other vehicle and create that damage because i was not driving fast due to the rain, the vehicle was already on stop when i had the impact plus i only hit the corner of the vehicle which did not even suffer any damage! if the impact was that much to cause it to hit the car in front and create a big dent in its rear, then the vehicle i hit should have suffered more than just scratches. eventually the officer made us sign the report and which i inderstood that i had no obligations with any of the other two parties and they just need to settle between themselves. and now i received a notice from an insurance company asking me to pay 164k! i have no capacity to pay that amount of money esp for something that i know was not my fault! is there any advice you can give me on this? i appreciate your help