My prefix prefix was a clown,
My infix infix gets around,
My suffix suffix is long dead,
You don't want me on your head.
My prefix prefix was a clown
Bobowas a famous clown, (Thanks @hexomino)
From your double use of prefix I think the actual prefix is CO
My infix infix gets around
Using my thinking from the previous clue, I think this is Meme,
as they are spread around a lot. And therefore the infix would be ME
My suffix suffix is long dead
The Dodo bird has been famously extinct for a while,
Making the suffix DO
A hairy black or white problem
A comedo is a clogged hair follicle, which can cause white heads or black heads. (Thanks @SecretSquirrel) And you don't want them on your face.