Sounds like you may have Enhanced Messaging turned on.
With your message app open, click on the overflow button top right (three verticle dots), click on Settings, then check that Enhanced Messaging is OFF. If ON, turn off.
Below that is Notifications for Messaging, which shoud be ON. Press and hold Notifications to get more features. Here you can change the default notification sound to whatever you have installed.
Both Pop-up Display and Preview Message can be ON or OFF depending on what you like.
Once you have the setting you like, close the app and then ask someone to send you a message, or if you have another phone, send from that.
