I can't update my iPhone X to iOS 16

If your signature is correct and your iPhone X has not been updated since iOS 12, you're skipped about 4 years worth of updates. And when one does that, it usually requires updating iPhone using a computer, with either Finder (Mac) or iTunes (Windows).

This link will explain how to update using a computer --> Update your iPhone, iPad, or iPod touch with iTunes - Apple Support

Instagram requires at least iOS 14 to run on iPhone. You need to update your iPhone, then you'll be able to use Instagram. Follow the directions in the link I provided.