Does anyone know of an app that will allow me to control Apple Music from my Galaxy Watch?
I don't think there'd be one. You can download AM songs with an Apple Music converter then play through Bluetooth. You can control the playback on your phone though.
You can only access music from Spotify and Google Play on the Galaxy Watch. but you can try use Apple Music Converter to convert Apple Music to MP3 or other playable formats then you can play your Apple Music on Samsung Galaxy Watch.