Try resetting your iPhone. This won't remove data, or change settings. If might help getting rid of the problem you're experiencing.
To reset, press and hold Home and Power button until the Apple logo appears. Then release both, and let the iPhone power up on it's own.
Did you update to iOS 9.0.2 over the air (Settings - General - Software Update)?
Maybe restoring through iTunes will help with your issue. Make sure there's a recent backup (iCloud or iTunes, whichever you prefer).
After restoring, reset your device once more, as described above.