iOS 11.1.1 freezes for no apparent reason?

I'm using the same iphone model and the same iOS version, and everything is fine.

Since you've already tried to restart your device (to no avail), I would suggest to restore your iphone to factory settings, so that you install a fresh copy of the latest iOS (11.1.1).

To do this, make a full backup of your device, then follow the steps provided in this support guide, setting your iP7 as new.:

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Then restore from your previous backup.

Regards

Giulio

I did all of that with a rep from Apple support on the phone and I'm still having the same issues, but even more frequently. It's very frustrating.