Once you have “Immunity” from “Criminal Prosecution” your Right to not incriminate yourself is MOOT and NON-EXISTENT, because YOU CAN NOT BE PROSECUTED.
Jail the LAWYERS and the WITNESS for Contempt, heavy Sanctions for the lawyers also, enough to be disbarred.
Immunity in a criminal case doesn’t shield you in a civil case, or compel you to testify.
And vice versa: Cosby is facing criminal prosecution for testimony in a civil case, where he was promised it wouldn’t be used in other civil cases
You also run the risk of violating an immunity agreement by saying something that contradicts your prior testimony.
Stomping your feet doesn’t change this.