If everything else is doing what you want, change this line:
$categories = get_categories('hide_empty=0');
To this:
$categories = get_categories('hide_empty=0&exclude=10');
Swap ’10’ with the category number you want to exclude.
If everything else is doing what you want, change this line:
$categories = get_categories('hide_empty=0');
To this:
$categories = get_categories('hide_empty=0&exclude=10');
Swap ’10’ with the category number you want to exclude.