Separated category links on posts

I’m trying to get different types of categories separated to fit this layout here on this blog here.

I want them each to be links to lists of all posts in those categories, but separated like you see in the image (so ‘Visual Language’ follows ‘Class:’ and ‘Freshman’ follows Year’, etc.) Any ideas?

All my categories are set up as follows:
Older Works
– Film
– Graphics, etc.
School
– Drawing
– Visual Language, etc.
Year
– Freshman

I’m using <?php the_category(); ?> after each post to show its category, but it’s showing them all, as you can see. I was wondering if there was something for the_category like child_of for wp_list_categories but I can’t find anything like that. Any ideas would be awesome.