If the car that rearended you without being hit by the third car first then the car in the middle is At Fault for your damage and the third car is at fault for the damage to the rear end of the middle car. The first car is not at fault for the quick stop.
The car to the rightAnother View: Above answer is incorrect. If the intersection is uncontrolled by any signs or signal, the car which approached the intersection from the bottom leg of the tee (i.e.: the road which ended at the intersection) yields to the through-roadway.
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