The US Federal Vaccine Court spends $1B per year in payouts to vaccine injured people. You do not sue to have your case handled there - you get assigned to it when your shot and symptoms fit the profile. It was set up at the same time the drug companies were protected from lawsuits.
https://www.uscfc.uscourts.gov/settlements_and_ADR

The most recent year's report discusses a strange and dramatic increase in people being assigned there for the annual flu shot. Imagine that.