Yes—you may file for a third-party claim (i.e., sue the other driver or their insurance company for damages, including non-economic damages) if your injury is considered a “serious injury.” This is defined as:
Broken bones
Miscarriage/loss of fetus
Permanent loss or loss of use of an organ, bodily function, or bodily system, and/or permanent consequential limitation of the use of same
Non-permanent injury that prevented you from performing your usual daily activities for at least 90 of the 180 days following the date of the injury
Injury that results in significant disfigurement
Injury that results in dismemberment or limb loss
Injury that results in death