Hi Emma,
We see you're trying to add a song as your alarm in the Clock app currently. First Restart your iPhone, and try the steps again to add the song. Also, be sure your device is up to date with the steps in Update your iPhone, iPad, or iPod touch.
Then confirm you're going to the correct path to add the song: Clock > Alarms > Sound > Songs > Pick a Song.
You've mentioned downloading the song, go to Settings > Music > Downloaded Music to confirm the download was completed. If you don't see the song here or in the Music app you see an iCloud icon next to the song, it means it wasn't downloaded. The song has to be downloaded on the iPhone in order to be used.
Are you using the same steps in this article to Redownload music?
Are you able to add other purchased songs/tones to the alarm?
You can also use Garageband to create tones: Create a ringtone of your Logic Pro or GarageBand for Mac song
Take care!