Self-installing applications

Hello, for some time now I’ve been having an issue with my phone: apps are installing by themselves without me asking for anything. I’ve tried uninstalling the recently installed apps, but I think some remnants have remained on the phone. I believe they can install themselves because every time I go back to the settings, the box preventing apps from unknown sources from installing is always unchecked (even though I check it again every time). I installed Avast, which only detects this “box” problem, but I can’t fix it if the box never stays checked.. does anyone have a solution? So many apps are creeping in that my phone isn’t functioning properly and even refuses to unlock again.