jdrama / jmovie about a celebrity

You could watch "Kiseki: sobito of that day". It's about the Japanese group Greeeen. 

Reinoryokusha Odagiri Kyoko no Uso (2010) Comedy / Mystery

I can think of 3 dramas that might fit what you're looking for! They're all comedies.

Papadol - Ryo Nishikido (from idol group Kanjani8) plays himself, and idol who marries a single mom and has to keep their relationship a secret from the press.
Ikemen desu ne - A girl secretly takes the place of her rockstar twin brother in his boy group when he gets injured. It's a remake of You're Beautiful, a pretty popular kdrama.
Mendol  - 3 girls who want to become idols witness a crime. To protect their identities, they disguise themselves as boys and become a popular boy group 

movie - well probably not celebrity in the term of what you looking fro

2LDK -  two  actress(senpai and kouhai) with different personalities and feeling toward other put to live in the same apartment room by their agency that bizarrely led into some crazy violence

Detroit Metal City - kenichi matsuyama hilarious played the  shy, softspoken pop music lover negishi and the totally oposite persona, the charismatic death metal vocalist, johan krauser II

Kisaragi - the mysterious circumstance of the death of "cult  c-list model" led their hardcore fans into some bizarre encounter, solve the case hilariously (or at least make the sense for them)

nana - mika nakashima as band vocalist

the long excuse - the protag is famous novelist and sort of tv personality

the snow white murder case - there's no celebrity, just show how badly can media accused someone as culprit then ruin the life

no more cry!! - there two brother separated when they were kid.  years later the younger brother become famous comedian

if you are into anime the Perfect Blue is perfect fit imo .

The liar and his lover is a beautiful movie starring Sato Takeru. Another movie I know would be Bandage, starring Akanishi Jin. Loved it when I watched it but it's been ages... but The liar and his lover is definetly worth a try!

They both focus on the music industry/ the people in that industry.