I previously purchased songs and then deleted them from my phone. I can't get them to download back on my phone and they say purchased when I look them up in the store.

See if they are showing as purchased on your iPhone using the iTunes Store app, by tapping on ellipsis at the bottom then Purchased.

If not, in the Music app, tap on your profile, scroll up and tap on Account Settings and see if there are any hidden purchases.

Or, open the iTunes Store, scroll up to the bottom and sign in with your Apple ID and look for hidden purchases.