Can I update my iPhone X from IOS 15.5 to IOS 16.3.1?

Yes you can, and should to get the latest features and security updates.

Go to Settings > General > Software Update.

This link will show you how to update your iPhone, iPad, or iPod touch using WiFi -

Update your iPhone or iPad - Apple Support Update your iPhone or iPad - Apple Support

This link will show you how to update using your computer -

Update iOS on iPhone - Apple Support Update iOS on iPhone - Apple Support

I wouldn't!! I have a 10 and the moment I went to v16.3 my screen stopped responding to touch frequently. When I reported, went to Apple Store, etc. nothing could be done to fix it. Next day v16.3.1 released and I installed it. Screen touch worked for most of the day, but all calls were so choppy neither party could carry a conversation. Today touch screen is hit or miss, calls still bad. These v16.3 releases are not ready for prime-time IMO!!!! A doctor I work with that has a new iPhone 13 (yeah, he chose not to get 14) has the same problems after "upgrading" to v16.3. Best way for me to send messages now is to tie them to the phone and throw the phone to the recipient.

Probably a billion people have updated by now.

Yes of course you can update. The update had no effect whatsoever on battery health or usage on my X.