There may be a problem with the touch screen and IOS 9.0.2. The screen can freeze. A possible quick fix without data loss is to depress and hold both the 'sleep/wake' button with the 'Touch ID button' until the Apple logo shows. I know this is mentioned in other posts when answering a question, but it might take sometime to find this help as the question may not always represent the way in which you might ask it.
NB BEFORE GOING BEYOND THIS QUICK FIX EG FULL HARDWARE RESET. ENSURE YOU FIRST TAKE A BACKUP