Sync Photos without iTunes?
Use iCloud Photo library it'll sync pictures automatically between Mac and iPhone (it does also work with iPad, Apple-tv 4 and iPod Touch 5/6) with iOS 8.1 or newer.
You can try to import using the native photo app on OSX.
Connect iPhone to Mac via a cable, open photos on Mac, select the import tab in the tab bar or in sidebar.
You may have to give the computer access to your phone.