Missing songs after 8.0 update and sync

I did the iOS update a few months back and noticed that the songs I had downloaded in May and June 2014 were missing. Since the computer I used that had iTunes was stolen in July 2014, I had no way to access iTunes. Finally tonight I was able to plug in my phone to iTunes on the computer. The playlists showed up with the missing songs in them. I then selected sync hoping they would be moved to my iPhone 5, Instead my playlists are now empty. Is there a way to get my songs back?