Hello BritniGraham,
Thanks for posting in the Apple Support Communities.
This sounds like you may be accessing the Now Playing feature with the Apple Watch, so let's see if you may be selecting your iPhone to play the audio. You can locate additional information here: Use Now Playing on Apple Watch - Apple Support
Use Now Playing with a different device
If more than one device is available to play audio—an Apple Watch, iPhone, and HomePod for example—the name of the device you currently control appears in the top-left corner.
Tap < to see a list of devices, then tap one to control it.
If you're seeing this occur directly in the app, check to see if you have an icon in one of the corners to control which device plays the music. If you need additional help with the app, we'd recommend reaching out to YouTube Music Help.
Have a great day!