There's a few things that could be wrong with what you're doing. What template are you trying to modify? I'm presuming you are working on the single.php template file? If so, you can use
c2c_get_current_custom() instead of
c2c_get_post_custom() since the latter requires that you first explicitly provide a post ID, whereas the former will use the current post (assuming you are in the single.php or page.php template).
Also, you are sending a variable,
$field, to the function, but have you set that variable? If not, you should just send the name of your custom field, i.e.
Finally, you don't need to put the shortcode (the
[custom_field field="ommig" /] bit) inside your post if your intent is only to set the class for that div. The shortcode will just insert the value of the custom field into the body of your post.
So... ultimately you probably just want to replace the example code you provided above with:
<div id="header" class="<?php echo c2c_get_current_custom('ommig'); ?>">
Then for a post, create the custom field called "ommig" with a value (which it sound like you've done already).
This particular set of code only makes sense and works properly if you are working in single.php.
Hope that helps.