Touch ID not working after 9.0.2 update
The touch ID data is stored in the secure enclave so the data storage there and the update of iOS is really not related in any direct way with the functioning of that software and hardware.

You can troubleshoot this the same as most iOS issues where you don't know if it's hardware or software by making a backup (or two - one to iCloud and one to iTunes) and then erasing all content and settings and then trying the "problem" task. In your case, after removing all your data and settings, you would test one or two fingerprints by adding them.

If that fails, then restore the iPhone from a iTunes. Repeat the test. If it fails, you have a hardware issue. If it works, then you can try loading your data from the backup and then trying one final time to see if the hardware and OS that work to save your fingerprint also work with your apps and settings.