I accidentally deleted the music app and now there's not enough space to put the same exact music back?

While deleting a widget and rearranging my homescreen, I accidentally deleted the pink Apple Music app. Even though it prompted me with a confirmation, I was in a rush and accidentally said yes.

I downloaded the same app again but now itunes says this:

The Iphone cannot be synced because there is not enough free space to hold all of the items in the iTunes library (additional 17.57 GB required).

What I don't understand is why there is not enough free space now when just a minute ago my entire music library on itunes was on my phone.

I would appreciate any help and advice. I use my music especially my 40< playlists for work and don't want to have to redo all of them over. Also I have tons of music which I do not wish to lose and really need to play via my iphone.

Thank you so much!