Is a personal injury settlement limited by the amount of the at fault driver's policy liability limit?

Not necessarily.  Check your own policy to see your limits of something called "UM UIM" for un-insured motorist, under insured motorist.  You can actually get insurance to protect yourself in case you are injured by a motorist that either doesn't have insurance, or is under insured.  you choose the limits for this insurance, and it means you can collect from your own insurance company.