iPhone 5c unresponsive screen

My iPhone 5c 8GB out of the blue started to have an unresponsive screen, the phone is almost a year old now, but very good condition, with no scratches on the screen because i've had a glass screen protector. sometimes it would sense touch enough to unlock it, but still start to open apps and type on it's own. The home and lock buttons work fine. I have done a whole system restore and update. Is this the screen or a software problem?