Welcome to Android Central! So you're only talking about the unread badge notification on the app icon? Are you still getting notifications in the status bar?
Are you still using the stock TouchWiz launcher, or did you install a 3rd party launcher like Nova?
Try to clear the data and cache of your messaging application, it should be under settings > application manager > from there select the messaging application that you are currently using. Once the data and cache is cleared reboot your device.