If the following are all good then you may have to make a Genius Bar appointment with the nearest Apple Store to have them diagnose the problem for you.
1. Volume buttons
2. Mute switch
3. Do Not Disturb
4. Connected to a Bluetooth device
5. Sound & Notification settings set accordingly
6. If using a 3rd-party messaging app, make sure that to toggle "Allow Notifications" for it in the notifications settings.