Should people be allowed to sue a vacciene company if they get very bad effects from it?

I think if the answer is yes, more people would be willing to take the vaccine.

Define very bad effects. 

Some examples:

Any negative effects from the vaccine that you experience.  If you get a sour arm for a day, you won't win much in court since you would have to pay the legal fees of the lawyer.

Well, you can't. They're all immune to high degrees (all of the Covid vaccine companies).

Pfizer and Moderna are completely untouchable, only the governments can be sued.

The only Covid-vaccine company that agreed to partial liability in the whole world is AstraZeneca and that is mainly only in its homeland of UK though it agreed to semi-liability with certain nations.

Good answer.

Perhaps we should be paid to have the vaccine....Keep the money out of the pockets of fat cat lawyers.

In a class action lawsuit yes, not any individual. Ethical considerations aside, there is no practical way it would work because each individual case would have to demonstrate causality, which would take far too many resources.

A sore arm is a natural effect of someone jamming a piece of metal through your muscles and injecting a bunch of fluid into it. Just hearing that case would be silly.

Just out of curiosity for those who have submitted to the vaccine, did you sign anything or given anything to read that showed what was in it or possible side effects?

I agree with you, vaccine companies need to suffer for the damage they caused