Can You Get Punitive Damages On A Personal Injury Lawsuit?
It depends on the state, but generally punitive damages are limited to intentional and malicious conduct.
So, where the cause of action is based on negligence or nusiance, probably not, since those are usually not actions committed with the deliberate intent to harm the plaintiff.
All laws vary by state. Check your local listings.

Yes. Collecting on them is another matter. “Reverend” Al Sharpton –of the presidential campaign fame– had a judgment entered against him for slander a decade ago. He’s never paid a dime.
In CA, yes you can.