In normal use Messages on your Apple Watch should mirror the paired iPhone. If the devices are working close together the message is received by the phone and forwarded to the watch over Bluetooth. If your watch has cellular function it will switch to standalone cellular only if it can’t communicate through the iPhone.
This suggests your watch is a cellular model, and your iPhone is having problems communicating. If it is not receiving text messages the problem is probably a software glitch or between the iPhone and the cellular network. I suggest you begin by restarting both devices then test again to see if anything has changed.
Restart your Apple Watch - Apple Support
Restart your iPhone - Apple Support