So you weren't syncing with iTunes on your computer? That doesn't really matter, since iPhones are usually set to automatically back up to the cloud.
Check the settings on your phone to see if your photos are saved to iCloud or not. Mine are all backed up to iCloud, which is also installed on my PC, so my pictures automatically save to the cloud and the PC (the photo stream ones). If your phone has been routinely backed up to the cloud (it usually does this automatically), the pics may be there as well.
Go into settings, go to iCloud, go to Storage and Backup. Check to see if iCloud backup is on. If it is, then it has been backed up automatically, and your pics are probably in one of your recent back ups.
'11 BMW E92 ///M3 - ZCP and DCT
'15 Ford F-250 - Lariat, 6.7 Powerstroke Turbo-diesel