Hey there hansen888,
It's possible you don't see the Downloaded playlist on your iPhone as it has been inadvertently hidden. We can check this by opening the Music app, going to your Library, and tapping the Edit button in the upper right corner. If Downloaded is not selected, select it now. Then, tap Done in the upper right corner and see if the playlist now appears in your Library. More information, including visual guidance, can be found here: View albums, playlists, and more in Music on iPhone - Apple Support.
If you want songs you add to your library from Apple Music to automatically download, enable the option under Settings > Music > Automatic Downloads. More details on this can be found in the Apple Support article Add music to iPhone and listen offline - Apple Support.
Happy listening!