Within Teamwork, you can choose to show only the items you have been notified of in the notification bell area.
Click your profile image in the bottom left of your site, and choose Edit My Details from the pop-out menu.
Go to the Preferences tab and toggle on Show only notifications for items I'm following.
Click Update to save your preference changes. Going forward, you will see an update under the notification bell area when you have specifically been notified.
For more information, see: Reducing Project Email Notifications