Hello Jchisholm3,
Thank you for using Apple Support Communities.
It looks like your iPhone begins playing music after you terminate a Bluetooth phone call in your car. I have several things you can try for this issue.
First, I would quit all the running apps on your phone:
Force an app to close in iOS
1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.
When you have done that restart the device and test the issue again:
iOS: Turning off and on (restarting) and resettin
If the issue persists, backup your device to iTunes, then restore it as new and verify that it works, after you have the second issue resolved.
How to erase your iOS device and then set it up as a new device or restore it from backups
If it does, then restore your backup to either verify it still works and the software just needed reinstalled, or isolate the issue to the backup file itself.
Happy holidays