I have all my devices (iPhone, iPad) syncing photos to iCloud. I can view all of them on any device (including MacBook Pro).
Your phone should be syncing to iCloud. I have sporadic problems with synchronization. The first step is to make sure you have the latest OS version on each device. Then log out of iCloud on each device and log back in. Make sure you are using the same Apple ID on each device, too.
Thank you. I’ll try that. I appreciate this a lot.