Nasty publicity to get you to have your cervix checked? (5,8)
I believe the answer is:
smear campaign
I'm afraid I can't even guess how this answer relates to the clue.
Can you help me to learn more?
(Other definitions for smear campaign that I've seen before include "attempt to bring discredit" , "Negative propaganda aimed at damaging a person's reputation" , "Organised vilification" , "Organised attempt at defamation" , "Manager is camp (anag)" .)