Iphone won't let me delete song?

I have the iphone 5c and my phone didn't come well made… The charger broke after 3 months and now it won't let me delete a stupid song! I "deleted" the song and than I listened to the top song but the song I just deleted was playing! So I went to the second song and it started playing again! So I went to the third song and the song that was at the top started playing even though The third song was completely different from the top song. Anyone know why this is happening? Ps I'm trying not to do anything to extreme measures

Its still in iCloud. So although you deleted it from your phone its still going to play from "The Cloud." You have to make a playlist with only the songs you want in order to not play that song