IPhone 5s touchscreen not behaving normally

Hello. For the past three months now my iPhone 5s' touchscreen has been behaving strangely. It sometimes doesn't respond at all, touches in the wrong part of the screen, will act like I'm touching it or typing when I'm not, and opens apps, goes through random pages when I'm on Facebook, and the keyboard double, triple, and quadruple types letters.

I recently visited my mobile service provider and was instructed to perform a hard reset and restore to factory settings. That obviously did not work (or I wouldn't be here) so now I don't know what else I can do. I'm more than six hours away from the nearest Apple Store, although there are many places that sell iPhones. What should I do now?