Does this happen when unplugged? If not, and it only happens when plugged in, it is likely the USB cable needs to be replaced. If it happens even when unplugged, does it have a screen protector on as B. Diddy asked? If so, try removing it.
If neither of those two suggestions solves the problem, then it's a hardware defect within the phone and should be either exchanged under warranty or taken to a repair shop. Connecting it to a computer and trying software fixes isn't likely to help. The screen responds to the electrical impulses in your skin, so anything that disturbs that detection (a defective screen digitizer, some screen protectors, loose internal components, broken USB cable shielding, etc.) can cause erratic touch response like you're seeing.
There is one other possibility. If you live in a very dry/arid environment, that can interfere with things too. We see an increase in these sorts of complaints in the winter due to low humidity levels. If that happens to be your case, there isn't much you can do except try to increase the humidity levels.