Lines on my iPhone 6s Plus and unresponsive touch screen

My iPhone 6s Plus fell flat on the back (it had on a tech21 case which is supposed to protect it from knocks and falls) and immediately lines appeared on the screen, with a quarter of the screen blacked-out. The touch screen is unresponsive. And when I press the home button, the display comes on with blinking lights. Calls to the phone says the number is busy.

I tried to back-up the phone and my pictures but because the iPhone is locked, it is not able to back up on the computer and iPhoto says my Mac is not authorized to access the photos.

It is has been updated with the latest iOS.

Any ideas as to how to resolve it. It is within warranty but I live in a region with no apple support. Is there something I can do? I have left it on to let the battery run out, don't know how that helps.