Hello and welcome to Apple Support Communities, TrumpetMonster.
If I understand your post correctly, once you select a song it repeats over and over on your iPhone. I can understand wanting to be able to shuffle music or play a playlist. I'd like to help.
It sounds like you've done some great troubleshooting so far. Let's check to see if repeat is selected on your iPhone. Open Music and select a playlist. Once a song is playing, tap on the song at the bottom of the screen. Scroll down until you see the shuffle option. Tap the option to select repeat, repeat one song, and turn off shuffle.
Check out this guide for more information:
Play music on iPhone
Let us know if that resolves this issue for you.
Thanks for using the Apple Support Communities. Take care.