Hello Tammys321,
I understand your Apple Watch is no longer charging, and you have some questions and concerns about the charging adapter you're using. I'm happy to help you out with the issue you're experiencing and answer your questions.
Although the wattage of the adapter may be higher depending on which model of iPhone you have, you should not experience problems charging your Apple Watch with the Apple USB AC wall adapter that came with your iPhone. Apple Watch batteries do chemically age over time just like you would experience with other device that has a lithium-ion batteries, so it is possible that you may at some point need your Apple Watch battery serviced. However, I recommend trying out the steps in this support article first: If your Apple Watch won't charge or it won't turn on. Also, if you would like to learn more about your Apple Watch battery and how it affects performance, take a look at this: Apple Watch Battery and Performance.
Thanks for using Apple Support Communities.
Take care.