Just turn off all Facebook notifications for the Facebook app.
Do you really need those notifications when you are not in the app?
I mean, really.
All of your notifications are stored right under the bell icon anyway.
Just get to them when you open the app.
Your device may differ, but the general gist is...
Settings
Apps
All apps
Facebook
Notifications
(turn them off, or select the lowest priority, usually 0)
And yes, do the same thing for Messenger.
To eliminate the problem if this doesn't work (it should), uninstall/disable the Facebook app and just use your browser to access Facebook instead.
This can also save a large amount of space on your device.