My iphone 6 touch screen has become intermittently unresponsive

My iphone 6 started becoming intermittently unresponsive on 10/3/2015 and this was the first time I ever had any problems with it (over a year of use). It is not damaged in any way, and there is no apparent explanation. The touch screen will work for a few seconds and then become unresponsive. Apps will start opening on their own like my phone is possessed or something. My battery is draining much quicker then usual. Frankly, the phone is acting like there is "some process" running in the background that is sapping all the system resources. I have soft reset the phone more then 10 times, reset the system about 5 times, and then finally setup as a new phone. I am strongly feeling that it is an IOS 9.0.2 issue that needs to be corrected, because my coworkers iphone 6s that is brand new has almost identical behaviors. Please help me.