I am looking for a comprehensive listing of all celebrities (including
athletes) who have endorsed (paid or free) pain relief products. I
would like to know: name of celebrity, name of product they endorsed
and what year(s) their endorsements took place. Thank you.

Just a general comment, it is virtually impossible to come up with
lists that include "all".  Obviously there are the outliers like
foriegn companies/foreign drugs, but even if you say just in the US,
the list probably does not exist.  I think researchers would be hard
pressed to create a list of all pain relief products let alone all
endorsements for them.

To put it another way, asking for something that does not exist is
probably not going to happen.

I would suggest asking for lists of endorsements and stating how many
references would be acceptable....  50 endorsements, 100 etc.