Hello 1grammiP,
If you've already turned off the Do Not Disturb mode, check to make sure that you don't have any Focus enabled on the device in Settings > Focus.
Use Focus on your iPhone or iPad
Also, make sure that you have the Ring/Silent switch on the side of the device set to Ring mode (pushed towards the front with no orange strip showing).
You can then go to Settings > Sounds & Haptics > Text Tone, to set a sound. On the main Sounds & Haptics page, make sure the volume is turned up to the level that you want.
Change iPhone sounds and vibrations
If you've set a notification sound in there and it's not playing, check in Settings > Notifications > Messages, to make sure you have Allow Notifications turned on.
Change notification settings on iPhone
Cheers!