Hi Tsinoy Newbie,
One important piece of information that you didn't include was whether or not the iPhone also shows the unread badge indicator.
If it does, then there is likely a message that is being recognized as unread. Checking deleted, junk or unknown sender lists would be a good place to start in examining or locating that item.
If not, you may try refreshing the Mac Messages application by first fully closing/quitting the app. Then, hold the Shift key on your keyboard while clicking the icon to open that app again. This combination forces an app to ignore saved-state information as described at Prevent apps and windows from reopening on Mac:
"Other solutions
- Press and hold the Shift key while opening the app. This doesn't change any settings, but the app forgets any windows that were open the last time you quit the app."
Regards.