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?

Thank you,