Can I just get text messages with alert sound on my iPhone and not Apple Watch?

Hi

How notifications behave depends on the status of your devices and your settings. With Wrist Detection enabled, in order to bring notifications to your attention as soon as possible:

- If your iPhone is unlocked, you will receive notifications on your iPhone instead of on your watch.

- If your iPhone is locked or asleep and your watch is unlocked (regardless of whether the watch screen is asleep or awake) and on your wrist, you will receive notifications on your watch.

- If your watch is locked or has Do Not Disturb enabled, notifications will go to your iPhone.

More information:

About notifications on your Apple Watch - Apple Support

If you would prefer not to receive text message notifications at all on your watch:

On your iPhone, in the Watch app, go to: My Watch (tab) > Messages:

- Choose Custom;

- Turn off each of Show Alerts, Sound and Haptic.