I had this issues for weeks now, freezing touchscreen was only the beginning. Two weeks ago there were phantom touches which were creepy and made me think I had a virus. This thread led me think iOS 9 was the reason, waiting for a fix.
Showing my phone at the Apple Store was not a success:
I couldn't demo my problems, everything worked normal. Plus I was out of warranty with my September 2014 iPhone 6 Plus.
but they did a touch screen check where I to play a "paint it blue" game to test the display. It showed some defects so they offered me a display exchange for 135€ But recommended trying a free repair by my provider (which turned out to be complicated/impossible after the first year of warranty).
The next week or so it got even worse, couldn't even take some calls because of the defect. I tried iOS 9.2.1 beta, did a complete reset, tried to deactivate some suspicious services mentioned here, no success.
I recognized that the problems occurred in situations where I had bad signal. The Apple Store was in an area with particular good signal. Back in the garage my phone went crazy again.
So today I went there again to let it get fixed, the test was repeated - no error this time but I insisted that it was a real problem.
4 hours later I got it back, no problems so far.
The apple technician told me phantom touches symptoms were always fixed by a display exchange, so no need to exchange the main board, too.