Hi there Foxc3,
It sounds like for some reason you are unable to add a purchased song from your music colllection to a playlist. I would start by quitting all the running apps on the phone:
Force an app to close in iOS
1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.
When you have done that restart the device and test the issue again:
iOS: Turning off and on (restarting) and resetting
This should refresh the Music app to allow you to be able to add the song to your playlist as long as it is not a smart playlist which adds content to itself based on criteria you set when you created the playlist.
Thank you for using Apple Support Communities.
All the very best,
Sterling