The surest way to resolve this is to create a fresh Photos Library by following these steps:

1. ⌘ cmd-Q out of Photos.
2. Go into  → System Preferences → iCloud → Photos Options… and uncheck iCloud Photo Library.
3. Reboot if you want to be safe, though it shouldn’t be necessary.
4. Launch Photos with ⌥ opt-click.
5. Click Create New… and name your new Photos Library.
6. Go into Photos → Preferences → General and click Use as System Photo Library.
7. Go into Photos → Preferences → iCloud and check iCloud Photo Library.
8. Wait for your photos to be redownloaded from iCloud.

If you’d rather try to keep your existing Photos Library, follow these steps instead:

1. ⌘ cmd-Q out of Photos.
2. Create a backup of your Photos Library.photoslibrary file.
3. Launch Photos with ⌘ cmd-⌥ opt-click.
4. Click Repair.
5. Wait for macOS to repair your Photos Library. A full sync should take place once the repair has completed.

Some screenshots courtesy of OS X Daily.

Photos can have any number of Libraries, but by default, it opens the last open library when you click on the Photos icon. To open other Libraries, hold down the Option key when clicking on the Photos icon. This will pop-up a dialog, showing you the available Photos libraries.

Photos sync's new photos from iCloud (say from your iPhone or iPad) to only one of the libraries, and that library must be declared as the System library. Perhaps you are not seeing new photos because the library that is opening is not the System Library.

You will see which Library is the System Library when you hold down the Option key and open Photos: that library will have 'System Photo Library' next to it. This one will have your new photos in it.

If you want a different library to be the System Library, simply open that other library (as mentioned above), then in Photos, choose Preferences>General> Use as System Library. This will cause your iCloud photos to sync with this Library.

There is no a way to browse all images across all libraries, each are separate. Photos does not have a way to open multiple libraries at the same time. If you only want one library, you can simply import photos from the other library into your System Library, by using the Import function, and navigating to the other Photo library, typically found in your Pictures folder.