Hello Amanda,
I wonder if you are seeing your iTunes in the Cloud purchases. The items you see with the iCloud icon next to them are purchased songs that you can stream from iTunes in the Cloud. You can hide these songs in Settings on the iPhone:
Just show music that’s been downloaded from iCloud: Go to Settings > Music, then turn off Show All Music.
These steps are from the iPhone User Guide:
iPhone User Guide
http://help.apple.com/iphone/7/#/iph6e2dfb83
If there are just specific songs you would like to hide, you can hide them using the iTunes Store on your computer:
- Open iTunes on your Mac or PC.
- From the Store menu, choose Store > Sign In, and then enter your Apple ID and password.
- Go to the iTunes Store.
- Click Purchased from the Quick Links section on the right side of the iTunes Store.
- Choose a content type by clicking on Music, TV Shows, Apps, or Books from top.
- Hover your cursor over the item you want to hide.
- You will see an "X" either to the right or left top corner of the item.
- Click the "X" to hide that item. A confirmation dialog will appear once you click the "X."
Once you hide the songs on your computer, I recommend quitting and relaunching the Music app on your iPhone. You can find more information about hiding purchases here:
iTunes Store: Hiding and unhiding purchases
http://support.apple.com/kb/ht4919
If the songs do not display a cloud icon next to them, try deleting them directly from the iPhone using these steps:
- Tap the Music app.
- Tap the Songs category.
- Swipe left to right over the song you want to delete.
- Tap Delete.
How to delete content you've downloaded from the iTunes Store, App Store, iBookstore, or Mac App Store
http://support.apple.com/kb/HT5772
Thank you for using Apple Support Communities.
Best,
Sheila M.