Before going any further, open your Gmail and go to the "All Mail" label, just to make sure there aren't some older unread emails that you may not have been aware of.
If you've confirmed that all mail has been read, you can try something that's a bit more drastic, which requires you to set your homescreens up again. Go to Settings>Apps, tap Menu>Show System, and look for the Samsung launcher app (I'm not sure what it's called now -- used to be TouchWiz, but now that the UI is called Samsung Experience, it'll be listed as something different). Select it and Clear Cache/Clear Data. This will wipe your homescreens and your launcher settings, which means you'll have to set everything back up -- but it has helped this type of issue in the past.