I think you are incorrect. There’s a Court for vaccine damages, paid out by the US Federal Government.
https://www.findlaw.com/healthcare/patient-rights/can-i-sue-vaccine-manufacturers-.html
https://www.congress.gov/bill/99th-congress/house-bill/5546
https://www.hrsa.gov/vaccine-compensation
Good info. Thanks for the correction.
I can’t remember where I saw it, but an article regarding vaccine damages paid by the US Govt has a reputation of making it almost impossible to get any compensation because they claim a person can’t prove it.