I think you are a:

>! tooth!

I live in a palace where it's dark inside  
No light in there, unless open wide  

>! Teeth live in mouths, which fit this description

Even though I am not a king, sometimes I wear a crown

>! Teeth sometimes have crowns

I am not a queen either, neither I am a clown  

> ?

I'm known for tearing stuff by moving up and down

>! This describes chewing food

Don't take care of me and I might hurt you

>! If you don't brush and floss your teeth, they'll start to hurt!

Take care of me and get better pictures of you

>! People like to have a dazzling white smile for photos!