Thanks for posting and sorry for the delay ― let's see whats going on.
A few questions: is your TV connected to the same network as your device with the YouTube app? Does your TV have a built-in Google Chromecast? Also, were you able to play YouTube on your TV before?
Give these steps a whirl:
Make sure that your TV is connected to the same network as your casting device.
Try to update your TV's software
Let us know how it goes.