With iOS 10 my screen no longer works?

Just recently I updated to the new iOS 10 and since I have done that my iPhone has been acting very strange. It will start scrolling and tapping on things by itself. An example being me trying to type a message and random keys will be pressed even though I am not pressing them. Also the app will scroll up to previous messages or open pictures without me even touching the screen. Another example is while I am at the home screen, it will swipe to different pages without me touching the screen. So I down-graded back to iOS 9.3.5 hoping that would solve the problem, since I was not experiencing this problem before going to iOS 10. Once I was back on 9.3.5 the problem still persisted. I then tried hard rebooting the device multiple times but the problem was still there. I have heard of iPhone screens going bad, but I have never heard of an instance like this. I have ordered the iPhone 7 Plus and was going to trade in my current 6 Plus, but I am now worried it won't have the same value with a broken screen. Any advice on how to fix this as soon as possible will be greatly appreciated. Thank you.