Display Issues

So I am looking for some advice, because at this point I am at my wits end. I have a new Iphone 6 plus and I am constantly having multi touch issues. I go to touch one part of the screen and either it registers somewhere else, doesn't respond, or causes the screen to jump around and open random apps/message or even randomly call people. I generally send and receive quite a few emails and text through out the day and this problem is making it very hard for me to use my phone.

I have had the screen replaced, wiped the operating system back to zero and started over, without using my back up and with my back up, and most recently I even got an entirely new phone as a swap from my last trip to apple.

I find it hard to believe that I got two bad phones in a row, but I don't know what could be causing the issue.

The phone is now roughly two weeks old.