How to update my iPhone x?

The current version of the Instagram app requires iOS 15.0 or later. For the iPhone X, the latest release of iOS 16 is the end of the line. So if your iPhone is up to date, you should be able to install the Instagram app. If there are any problems with it, you would need to contact the app developer.

About iOS 16 Updates - Apple Support

Update your iPhone or iPad - Apple Support

Updating iOS: common issues and solutions - Apple Community

Instagram is not an Apple Product. Contact the app developer here --> App Support  or Instagram Help Center