My phone was wiped clean and I switched carriers so it doesn’t have my original iCloud information but my watch wants my original iCloud information and it won’t let me pair unless I have that so what can I do about that?

If your Apple Watch is still working (not yet erased) you can probably get to the original Apple ID details on the watch, and reset the password if necessary.

If you forgot your Apple ID password - Apple Support

If the watch has already been erased you will need to follow the advice in Apple's support document,

About Activation Lock on your Apple Watch - Apple Support

particularly the section Turn off Activation Lock on the web

If you don't know the login credentials for the original Apple ID then you can't release the Activation Lock, and it will not be possible to reconnect your Apple Watch on the new iPhone.