Q: Apple Music on iOS 10 won't play Selena Gomez songs

Hi there tremblsi75,
 

Thank you for visiting Apple Support Communities. We'd like to look into Apple Music with you.
 

First, restart your iPhone and try playing a song again. See Restart your iPhone, iPad, or iPod touch.
 

If the same thing happens, let's see if you can play songs anywhere in Apple Music. Try playing songs from your Library, from the Apple Music catalog, and from Radio for example.
 

In the Library tab, you can find all of your music. The For You tab has music that's handpicked by experts just for you, and exclusive content from your favorite artists. The Browse tab shows you all of the latest hits and curated playlists. From the Radio tab, you can listen to Beats 1, our 24/7 worldwide radio station, and Apple Music's on-demand stations. And you can use the Search tab to find music that you want to listen to or see what other members are searching for.
 

From Use Apple Music in the Music app. 

If you have songs from your own music library on your iPhone, make sure iCloud Music Library is turned on, as well. See Turn on iCloud Music Library.

Let us know if these steps help. 

All the best.