You can’t sue the companies.
https://www.cnbc.com/2020/12/16/covid-vaccine-side-effects-compensation-lawsuit.html
There’s other sources but this was at the top…
But you CAN sue the pharmaceutical companies if you can show they failed to due care when certifying the safety and efficacy of the vaccine.
https://www.law.cornell.edu/uscode/text/42/300aa-22