Yes. Insurance companies are only liable to the limits of the policy. In many instances, drivers like yourself suffer injuries whereby the insurance company fails to adequately compensate the victim for his injury. When this happens, the injured party also sues the policy holder.
But the reality of it is in most cases, the policy holder does not have enough to cover the amount awarded in a settlement. You may win a "judgment" in court but if there is nothing to collect from the defendant, you'll get nothing. Most attorney's look into the financial health of the defendant before they decide to take the case because in most cases, attorneys in personal injury cases work on a contingency. If they determine that the defendant has empty pockets, they won't waste their time in a lawsuit. Good Luck!