Sadly, this sounds like your phone may be suffering from Touch Disease. You can check my profile; I have a link to a blog post that goes into more details.
You don't give us much info so perhaps you can share the history of the device (falls or impacts, broken screens, bent housing etc.) Your problem may be caused by something else but Touch Disease is pretty rampant these days.
Long story short, Touch Disease afflicts the iPhone 6 and 6 Plus (especially the latter). Eventually, touch fails outright but many people will see a gray bar at the top of the screen.
There are many repair shops that can do this kind of repair but just a few weeks ago, Apple announced a replacement program for the iPhone 6+(unfortunately, it's not free). Look at your options and then determine what is best for you.