My screen in my Apple Watch does not respond to my touch!

Oh-- there is another possibility: Sleep mode may be on. This locks the screen so you don't call someone when you roll over at night. It hasn't been a problem for me. When sleep mode is on, the symbol is this picture of a bed:

Same thing, though. Unlock by turning the crown knob or by pushing it in.

Sleep mode is part of Focus, and it's controlled through settings in iPhone>Watch or on the watch itself.

Use Focus on Apple Watch - Apple Support

One possibility is that you accidentally hit the water lock

This is pretty cool-- it keeps the watch from thinking it's being touched all over when you go swimming or take a shower. This symbol should be showing at the top of the watch if it's on.

It is unlocked by either turning the crown knob (pre os9) or clicking the crown inward (for watchOS 9)

This is an easy fix-- I hope it's what you need.