Hello there ShantyP,
We understand you're trying to change the audio output of your iPhone while using a direct connection to an external monitor or TV. Let's work together as we provide some additional insight.
To get started, not all apps or features may allow you to play audio to a different location. If it is available for the feature or app that you're using, tap the AirPlay icon while playing media as shown here: Use AirPlay to stream audio
If the app you're using to play audio from supports it, you'll be able to choose your headphones or compatible speakers from the AirPlay drop down menu of options.
If you don't see your headphones as an option, then that means it isn't supported by that specific app or media so you may want to offer feedback here: Product Feedback
We hope this helps.
Take care.