You can share photos to Flickr of Facebook using the "Share" button.
Or you can add them to Shared Albums in iCloud. If you have a Shared album, that has been enabled as a public webpage, you can share the photos on a webpage in iCloud. This page explains how shared albums work: iCloud Photo Sharing FAQ - Apple Support
The big problem is, you can add Photos to shared albums in Photos, but Photos does not let you enable the "Public Website" option. It does not show in the setup panel. I hope, it is a bug and not an intentional omission.
https://help.apple.com/photos/mac/1.0/?lang=en#/pht5f6df5f0
However, If you can create and setup the shared albums in iPhoto, Aperture, or on an iPad, iPhone, you can add photos from the Photos.app to show them on your iCloud webpage.
For example, I created a shared album in Aperture like this:

Then shared photos to it from Photos,

And the published webpage looks like this:

The shared albums will be very basic. There is no way to add annotations or to control the layout.