Hi
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:
- Your Apple Watch model - Series 3 (GPS) vs Series 3 (GPS + Cellular):
- The features of your carrier service plan:
- The type of connectivity that is available to your Apple Watch at the time:
About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support
Features and requirements that apply under various circumstances are detailed here, including within the footnotes:
How to use your Apple Watch without your iPhone nearby - Apple Support