iPhone Malfunction

That sounds like a failing screen. Sounds like it's time to make an appointment to have your phone evaluated by Apple.

Genius Bar Reservation and Apple Support Options - Apple

But, as you need to back up your phone before Apple does anything with it, now is a good time to do a complete back up and restore our phone.

That is symptomatic of a damaged or failing touch screen.

Make an appointment at the Genius Bar and have it checked and replaced if necessary.