It may help to follow the instructions here, including under the heading "Get help if you can't send or receive messages" and including unpairing and re-pairing your Apple Watch if necessary:
Keep in mind that the functions that are available on your Apple Watch when it is away from your iPhone depend on various factors including:
- Your Apple Watch model:
- The features of your carrier service plan:
- The type of connectivity that is available to your Apple Watch at the time:
Features and requirements that apply under various circumstances are detailed here, including within the footnotes:
If you still need help, then I suggest that you contact your carrier in the first instance.
If the issues persist, then, depending on your carrier's advice, I suggest that you next contact Apple Support (remote diagnostics and/or mail-in service may be available, if required), make a Genius Bar reservation or visit an Apple Authorised Service Provider for assistance: