I run OSX 10.10.3 on a Macbook Pro 15" Early 2011, with 8Gb RAM and 256Gb SSD.
Unfortunately I can only support your question. Exactly the same happened to me, the "Photos" and "Music and Sound" sections are empty. I uncovered this recently. I think I upgraded FCPX to the latest version (10.2.1), and removed iPhoto completely since then.
So I did in the recent past remove iPhoto, as the new Photos app is there. I also made sure I no longer have the old iPhoto Library; everything is now organized neatly in Photos.
iTunes is running as well, and I did download the FCPContent.dmg and installed it. I no longer have iMovie etc, but that was already removed long ago.
I also ran the old Garageband and the new one (v10), several times. This seemed to have helped others sometimes.
I uninstalled Final Cut Pro twice now, Final Cut Pro X 10.1: How to remove and reinstall Final Cut Pro X - Apple Support.
installing the additional content from a .dmg file every time (as the "download additional content"-menu item in FCPX just goes to the App Store, and then nothing is downloaded).
In addition I did find the content and dragged it onto the "Music and Sound" and als "Photos" section to no avail. Even individual files dropped there did not result in anything.
I really don't want to reinstall my whole Mac.
HELP?
PS other threads did also not solve this, not really:
Why can't I add final cut pro sound effects?
Neither the "Photos" nor the "Music and Sounds" browsers work