my itunes library dosen't show up on my iphone

For your iTunes library to visible on your iPhone, Home Sharing needs to be enabled on both iTunes on your computer and your iPhone (and it must be through the same iTunes account).

I'm assuming it's already enabled on your computer (since it is accessible from your AppleTV). To enable it on your iPhone, open Settings and scroll down to "Music". Under "Home Sharing" enter your Apple ID and password to sign in.

Then, to access the shared library, in either the Music or Video apps on your iPhone, select "More" then select "Shared" and choose the shared library.