iPhone photos aren't appearing on MAC at home

Verify that iCloud is set up for photos on your phone and your Mac. For the phone, Settings/[your name]/iCloud - Turn on Photos if it wasn’t on already. Then log in to https://icloud.com with the same Apple ID you have on your phone and verify that the photos are synced. Finally, on your Mac go to Menu, System Preferences and verify that iCloud Photos are enabled there also. See this for more info—>Keep your photos safely stored and up to date on all of your devices - Apple Support