Iphone 6 screen touches on its own

I have an Iphone 6, 64GB. I've updated to the recent software 8.3.

Randomly i'll be using my phone and the screen won't respond. Other times, I will be using my phone and I will be in the middle of typing a message and the screen will jump back and click a different thread and then it will go home and open another app and then go back to my messages and just jump around as if someone were touching the screen. It does not only happen while typing messages, it has done it on other apps such as calendar, Facebook, my fitbit app, and a few others.

I have tried to hard reset it, restore all settings, and even restored it from my computer but this still seems to happen and it will go for a few minutes before I can use my phone again. It has been happening since before I updated to 8.3, which was why I updated thinking maybe my phone was lagging since I had not updated.

I'm going to take it to Apple when I get a chance, but I was trying to see if anyone else has experienced this.

Thanks!!