Luckily our friend from CT who is not licensed in CA and may not know the law in CA made a correct guess. CA has a 2 yr statute of limitations for vehicular negligence cases where personal injury is involved. It is three years for property damage something our friend from CT forgot to tell you or missed.
Since you were hit by an uninsured driver you must make a claim against your carrier and demand to arbitrate the matter under same time frame as above. What we typically do is file an action against the negligent drive and if it was a hot and rum John Doe. We concurrently file a demand for arbitration under the uninsured provisions of your policy that way the statue is protected.
Lastly what did you receive the money from your carrier for? If you signed a release of all claims then you cannot proceed further against your carrier.
Hope that helps and good luck.