You are trying to add the photos to an album you created yourself? It is not possible to add photos to the albums created automatically by Photos for us, only to the albums we create ourselves.
Usually the photos should show up instantly in the album, when we add them.
Or is the album you try to add the photo to a shared album? When adding photos to Shared albums it may take a long time, if there is too much traffic at Apple's cloud servers or if your internet connection is poor.
If your album is a standard album and the added photos are not appearing there, you may want to check, if the album is damaged. As a test, create a new album and try to add photos to the new album. Does it work? Is it just a specific album that is acting up? Then Recreate the album and delete the previous version of the album.