Looks like you have a failed broadcom touch controller. Apple denies this problem even exists and offers no resolution to their customers who each paid $800 for that phone (at least) even though they nearly always fail at about 14 months old. Just outside of their one year warranty. They will tell you they will replace your device with a "refurbished" one for $329. Their "refurbished" phones are the phones that came to them as "unrepairable" just like yours plus the water damaged ones, ones that were smashed by a car, etc. The replacement phones often give the exact same problem within weeks of replacement. They don't see where there is a problem with the 6 plus but they moved and changed the way that chip is attached to the board on the 6s plus...
Now that my rant is over...
The chip can be replaced, a quality 3rd party phone repair shop will be able to replace it. If the repair shop says its not fixable, smile and thank them for their time and go find a quality repair shop... The new chip will eventually also fail, it is a problem with the placement and how its placed. the phone flexes and twists in that area breaking the connection between the board and that chip.
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