Sounds like Siri just really loves listening to tunes! Just kidding. It could just be that an app is set to auto-play.
Depending on the music app your phone is using, it might have auto-play settings turned on. Are you able to identify which app is playing the music?
If you know which app it’s using, try force closing it by opening the app and swiping up. Also check the setting to see if it’s set to play music when you shake the phone or at certain times. Then try restarting your phone.
Apple will stop supporting the latest version of IOS (IOS 13) on iPhone 6. It will still be supported on iPhone 6S, 6S+ and newer models. When this happens your phone won’t necessarily stop working but it will start to have more quirks. In short, it’s time to get a newer phone.