I apologize for not being able to come back until now. Anyway, I ended up replacing the libraries with originals from a new fresh save. I just saved them to my library and then placed them in the other save and now everything works. I need to add though that I also got rid of all lots and Sims I'd downloaded from the Gallery. You're right that the bookshelves in the Willow Creek Library were different in the Lil Simsie lot I'd downloaded, they weren't the original ones.
All I can surmise is either that's why the shelves in all libraries didn't have skill books or perhaps the Librarian Sim I had downloaded or one of the other lots. None of them were supposed to have CC in them, CC doesn't transfer from the Gallery from what I've heard, so I doubt it was a CC conflict. I don't have CC/Mods in my game and I never have. Though the problem is fixed for me now, it's still a mystery though because I had tried to replace those bookshelves with in-game ones that looked exactly like the ones in the original Willow Creek. Plus, the Windenberg Library was the original one, it hadn't been replaced and wasn't working.
I suspect the Librarian I downloaded. But I'm not sure... *shrugs*