Hi Yogabbababbas,
It sounds like your iPhone seems to skip music when you have these third party headphones connected as you exorcise. I know you said that you don't use the headphones that came with the phone, but does this occur when you do use them? If so, then it may be an issue with the headphones themselves. If not, then I would start troubleshooting the phone by quitting all the running apps:
iOS: Force an app to close
Double-click the Home button.
Swipe left or right until you have located the app you wish to close.
Swipe the app up to close it.
When you have done that restart the device and test the issue again:
iOS: Turning off and on (restarting) and resetting
If the issue persists, backup your device to iTunes, then restore it as new and verify that it works.
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.
Thank you for using Apple Support Communities.
All the very best,
Sterling