Generally, if an insurance company pays on a claim, you release the negligent driver and cannot recover anymore compensation. The family is usually not liable unless under circumstances involving negligent entrustment which is rare. If you had a prior attorney, that attorney would have probably looked at every avenue of recovery. Warning, You maybe countersued for a frivolous lawsuit if your lawsuit does not have merit. Contact an attorney.
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You "can" sue them, but you probably won't win. You may have signed a release when you got the money from their insurance, and that would mean you lose. If you go pro-se, the other side will probably win because you do not know the very technical procedures that must be followed. Unless they have lots of assets besides a house and cars, you probably wouldn't get anything even if you did win. So it does not look good, but I don't know all the facts, so I cannot say for sure. If you have not already done so, sit down with an attorney and go over everything.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.
Most of the time when you sign the insurance release you are are releasing the negligent party in their personal capacity, thus barring you from suing them personally. I would read over the release you signed or take it to a local attorney to explain it to you.
Large personal injury cases as a result of a car accident require a lawyer who specializes in this area. You should call a local lawyer and go over the facts of the car accident and your medical. The attorney should be able to advise you on how best to attack the defendant.