Very odd. Like phantom touches?
Do you have a case on the phone? Try removing it. Possibly something is exerting force on the screen or screen edge.
Did you try booting into Safe Mode to see if the behavior disappears? If so, maybe it's a rouge app issue.
Finally, you could try backing up your personal content and performing a Factory Device Reset, aks Factory Data Reset (FDR).
If those don't reveal the issue, then it probably needs to be serviced.
