Doesn’t this mean that I have to sue that nice old lady (teenager, nurse, fireman, etc.)?

Unfortunately, yes. If you were injured by a nice (and sympathetic) person who was negligent, and a lawsuit is needed, Georgia law requires you to file suit against the person individually, instead of against their insurance company. However, person who is being sued is probably not going to pay any of the Jury Verdict. In most motor-vehicle or premises liability cases, the insurance company will pay 100% of the Jury’s Verdict up to the amount of insurance coverage.