Bottom half of iPhone screen going crazy

I got my iPhone 5S November 1 and I loved it, but on November 4 i noticed that the bottom half of the screen was going crazy. It would be opening apps and pressing letters when i havent even touched the phone. If i hovered my finger over the bottom half of the screen it would sense my finger and open apps. during that time i could type and i could open any app on the bottom half of the screen that i wanted. I tried to search up if anyone else had this problem and i only found 2 peole that experience the same problem. That made me think that I just ended up with a defective phone because it wasnt common. also i think it was a hardware issue.

I was wondering if anyone else experienced this problem and what did they do. I ended up returning my phone and as soon as i get the refund ill be buying a new one. I didnt wanna have to get a replacement becasue i didnt want a refurbished phone. Hopefully the next one is fine. P.s. I tried the whole reboot and restore and nothing worked.

Here is a video of what happened. This isnt me but this is one of the people that i found experienced the exact same problem

http://youtu.be/zOnQsrdgURI