I dropped off an application at a local correctional facility for students after hearing from my friend (who is part of the staff I seek to join) told me that they are short handed. This was on Friday, and I haven’t heard anything from them. I also called their Human Resource Director to make a clarification on my job application, leaving my phone numbers. Then, last night, my friend put in a good word with the main director of the team that I’ll be working for.
My question is, should I make a follow-up call today?

I would wait until maybe tomorrow mid morning and call and ask about the status of my application. That way it gives them at least a day to look over it. You want to put your name out there but on the other hand you don’t want to sound too pushy.
Good Luck with it