If Play Music is 'the culprit', the headset won't work with ANY other players. But like I said, if it is the case, rebooting the phone should clear the issue. Sounds to me like this isn't your particular case.
As for the audio coming out of the earphones, that doesn't mean that there's not something wrong with either the headset or the jack itself. Thanks to all these controls you can have through your headphone jack (some accessories let you control camera shutter, notifications,etc.), the audio cables are no longer the only thing that run through your phone/headset. You can still have the audio signals properly wired and playing, but the control signals all jacked up, or viceversa. You can even try non-compatible headsets and you'll see what I mean (try a Nokia one into a Samsung... pressing the control button on the headset makes your audio go monoaural until released).