Hello mbd-w76,
Welcome to Apple Support Communities. We understand concern for your iPhone display not working properly after upgrading to iOS 15. Since you've already restarted it normally and force restarted it, the next step would be to make sure you have fully updated to iOS 15.0.2.
Update your iPhone, iPad, or iPod touch
If you have updated fully to iOS 15.0.2, restarted, and the issue is still present, next get a fresh backup of your iPhone. If you walk through erasing it to reinstall iOS 15, you will want to start with a new iOS install, not restoring from a backup.
Test your iPhone, then restore your backup if the issue resolves. Also make sure you've removed any case or screen protector installed, just to rule out that as a possibility.
If the issue is still present after installing a fresh iOS 15 with no backup restored, you may need to have your device looked at by a technician.
Find Locations - Apple
Take care.