Legal Question in Personal Injury in California

I think you're confused about the role of an insurance carrier. The insurance carrier pays for the debts of its insured, which in your case is the person responsible for harming you. The insurance carrier itself did not hurt you and does not owe you anything. The only reason the insurance carrier is paying you at all, is because it has to under the policy it sold to the person who hurt you.

I'm assuming that you got paid from the insurance carrier, and in order for that to happen, you signed a Release. It's pretty clear that you didn't read or understand the Release. If you were to read it, you'd see that the person you "released" was not the insurance carrier, it was the person who injured you. When you "release" somebody, that means you can never, ever sue them for any harm you suffered from that accident.

So in other words, the answer is "NO." You cannot sue the responsible party, because you already settled with him. But don't feel bad, because even when you sue, the judge or the jury very often make reductions, and you would not get a separate award for attorney's fees.