When did you create your AppleID? My Photo Stream is only available for users, who have been using it previously, with an older AppleID. For new users it is not available.
And if you have iCloud Photos enabled, My Photo Stream is also not available on a Mac.
If it is available for you, you can turn on My Photo Stream in the Photos > Settings > iCloud in the Photos.app on your Mac.
See: If My Photo Stream isn't updating - Apple Support
"If you recently created your Apple ID, My Photo Stream might not be available. Use iCloud Photos to keep your photos and videos in iCloud. Learn more about iCloud Photos and My Photo Stream."