Here's my story....
I had this problem 2 weeks ago, the touchscreen stopped working sporadically at first, then became constant, sometime it wouldn't respond at all or I would touch one app and another would open. I tried restarting it when I actually could turn it off but didn't hel[p.
I took it to my ATT provider and they told me to go the Apple store in Portland, OR.
So I off to the Apple store across town, after waiting an hour they said they were aware of the problem and gave me replacement phone, no charge.
2 days later...., the new replacement phone start doing the same thing, one again I have to go to Apple where they give me ANOTHER replacement phone. the said no way it'll happen again. I figure "ya, just a fluke, third times a charm...."
WELL,....today, after less than a week with my 3rd IPhone 6 Plus it does the same thing.
I love Apple products but I am so angry, Im a self employed contractor and need my phone to be working when I need it which is all the time.
So all that to say this..... I'm on my 4th phone in two weeks and am anticipating it happening again.....
Chris