There is another user on the S6 edge forum with the same, it seems that in her case she received the 5.1.1 update and while checking on the settings she changed something that it's suppose to allow to see the notifications with a single tap, I assume that it was something on the Accessibility menu. So, do you recall doing something similar? it will be good to see if there is a pattern so a bug can be reported.
But, back to your issue, according to her, she couldn't boot up on Safe mode because as soon as she tap the screen for anything it begins doing the same, so I'm afraid that if you find the same, you will need to do a factory reset in recovery Mode, try booting the phone and without touching the screen connect it to your PC and do a Full Backup with Samsung Smart Switch for PC (or Mac) and once you have that then do the Factory reset.
In case you don't know how to enter to recovery mode, turn it off (Like you were instructed above) and then press and hold volume up, home and power buttons until you see the Android robot, then browse the options with the volume keys and select with the power button.