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Hi Blan02, welcome to the community!
Could you please let us know which settings you have adjusted already so we can assist accordingly.
Do you have your phone on silent mode?
open the messaging app > menu > settings > notification settings > change the notification sound > restart the phone > check again.
Blan02 did you follow @Uliwoolys suggestion? Could you please let us know whether or not that worked for you.
Boot on safe mode and try again
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
are you using the preloaded messaging app or a third party app?
Settings > apps > all > messaging > clear data > restart the phone > check again.