Where you add your menu item title of your item, add this value:
$menu_title .= '<span class="update-count">' . $count . '</span>';
Well, he $count separately consider. I would have made it a separate function with a cache, and simply return from it's value. Then the code will look like:
$menu_title .= '<span class="update-count">' . get_my_count() . '</span>';
where get_my_count() is my function count that must be considered (as in the task of word).