Iphone 6 Plus White Line and Touch Screen Issues

My iPhone automatically updated a few days ago. It then could not back up to the cloud because of "network connection issues." Soon afterward, it became very slow. Yesterday the touch screen wouldn't work, almost as if the screen froze a few times. Today it began to happen much more often and for longer periods of time. Then a white line at the top of the screen appeared and the phone started to jump around as if I was trying to open different apps or access different areas of my phone, but I wasn't touching the phone at all. I haven't been able to make calls or send texts for 2 days. Is this a software issue? Will Apple fix my iPhone 6 plus? What do I do now?