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 top right of the screen, and choose Edit My Details from the dropdown menu.
Go to the Preferences tab, and toggle on Show only notifications for items I'm following.
Now, you will only see an update under the notification bell area when you have specifically been notified.
For more information, see: Enabling Notifications for Your Events Only