Okay, after spending hours upon hours trying many things, I managed to accomplish what I wanted, which was random images loading on each page in my header and linked to their own pages, using a plugin I already had installed: Custom Content Shortcode. I used a custom post type that I was able to hide from the WP search, which I couldn’t do with the Random Content plugin, and now, my random header posts and images don’t show up on a search. I may use Random Content for something else at some point, but it wasn’t right for this task.
I tried renaming the posts to some seriously random names, but the search still picks them up because the images inside are linked. I am now trying to at least redirect those links to the actual corresponding page,but am not having any luck. I will keep trying things and hope that somebody will post to tell me how to just hide this random content fro view.