Cellular for iPhone and Apple Watch

If you do not pay to add your Apple Watch to the iPhone cellular plan, then you can pair the Apple Watch to the iPhone as if it were a GPS ONLY Apple Watch.

In GPS ONLY mode, it will do EVERYTHING, an activated cellular Apple Watch will do, AS LONG AS the iPhone is nearby, where nearby is generally in the same moderately sized home, or on your person when you leave the house. And for less money a month. In GPS ONLY mode you can even use one of the cheaper celluar providers that do not support the Apple Watch, as in GPS ONLY mode, the cellular carrier does not have anything to say about your Apple Watch.

If at some later time you want to activate the Apple Watch cellular radio, you can do that, as long as your carrier supports the Apple Watch. In the U.S. it is generally $10 a month on top of your iPhone cellular bill (your mileage may vary)

No matter which mode you use your Apple Watch in, it will have a lot more features then you currently have as a dependent child controlled via your parent's iPhone.

In the U.S. phone numbers are supposed to be transferable.

So you should be able to disconnect from the family plan, transfer your phone number via your iPhone’s carrier, pair your Apple Watch to your iPhone, and finally get add-on Apple Watch cellular service via your iPhone’s carrier.

Standard Apple Watch to iPhone pairing

Set up and pair your Apple Watch with iPhone - Apple Support

When you pair to your new iPhone, turn off cellular in control center (Swipe up face from the bottom). The rest should be already be connected.