How do I sync iphone songs & music library to new PC?

I have an iphone6 and it used to be backed up to a windows PC through itunes. At that time I had my music library on the phone set to be managed manually where I could drag and drop selected songs from itunes to the phone. I have since lost the PC that I was using and I now have a new one. I have managed to only back up the phone to this new PC but I have not synced the phone to the new music library since this will reset/remove the songs/playlists/etc. that I have on the phone to match the PC. I would like to be able to once again manage my music library manually without losing what I already have on it on regards to songs and playlists. How can I do this?

Thanks.