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:
Read and reply to messages with your Apple Watch - Apple Support
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:
Features and requirements that apply under various circumstances are detailed here, including within footnote #1:
How to use your Apple Watch without your iPhone nearby - Apple Support
If you still need help, then I suggest that you contact your carrier in the first instance.
If the issue persists, 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: