Hey blimblob,
Thank you for using the Apple Support Communities! We understand you're not hearing an alert tone for new messages received on your Facebook Messenger app. Let's see how we can help.
It sounds like you've confirmed that 'Allow Notifications' is turned on for Messenger, as well as 'Sounds': Change message notifications on iPhone.
Next, check the Messenger application settings by following these steps: How do I turn Messenger notifications on or off? | Messenger Help Center
If you've done that, and everything is set up to be On for notifications and sounds, try the steps in this article next: If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open
Best regards.