IPhone has phantom touches to screen?

IPhone 5 has phantom touches to screen. When I do anything (text, facebook, pinterest) it starts going crazy and randomly selects things and starts typing, etc. I've done a soft and hard reset and fully restored it. I was hoping to figure it out instead of waiting for a new one. I'd prefer to resolve it with my phone. Any advice would be fantastic!

Added (1). And no my phone is not jailbroken. Also I keep reading that there are no existing viruses for iPhone 5 but it sure seems like one because it's EVERYWHERE not just in one app it's in my phone selecting random apps and screwing with my texts and emails.

It's not a virus. You have a problem with the sensors in the screen. Instead of having two layers, the pixels of the display and the touch sensors, the pixels do double duty-acting as touch-sensing electrodes while displaying the image at the same time. You need to take it Ito the apple store or where ever you purchased it from to get it fixed.

Same issue with our IPhone 4… Apple wants $130 to fix, it hasn't been jailbreaked. Very annoyed.

Yes I have have it on my iPad 3. There's no treatment. You have to get a new one. Sorry. Apple don't like products being repaired, so they make them unrepairable.