Yes. However, this right applies only in out-of-court settlements of personal injury claims, whereby you can renegotiate for a higher offer through a neutral mediator. You still retain the right to reject or accept the settlement offer even when your personal injury claim goes to court.
However, if the lawsuit proceeds to completion, the final value of your personal injury settlement is left to the discretion of the presiding judge. Such a settlement is usually more than adequate to cover medical expenses, pain and suffering damages, and any other cost that the judge deems applies to your personal injury claim.