Are your pictures in iCloud Photos? It sounds like they are-- if so, then if you create a Photos Library on your Mac (in the dialog from option-opening Photos), make it the System Library (in Photos>Settings>General), and connect it to iCloud (in Photos>Settings>iCloud with "Download Originals"), then in days or longer (depending on how many pictures you have) all the pictures in their proper albums will populate the new Library. If you keep the Mac Library connected to iCloud, then whenever you make a change on the Mac you'll see the same change in iCloud, and vice-versa. See
Set up iCloud Photos on all your devices - Apple Support
iCloud Photos isn't just a place to keep pictures; it synchronizes the Photos Libraries in all of your devices. Pictures all stay the same in iCloud, you Mac, your iPhone, and your iPad, and if you take a picture with your phone or iPad, the picture will automatically appear in the other devices. And if, on you Mac, you put that picture in an album, then it will go into an album on the other devices, too. And it's much easier to deal with pictures on the Mac than the other places.
Oh--and if you delete a picture from one device, it will be deleted from all. So keep a backup!