Solution 1:

Yeah I think this is a bug brought on by the new patch that a lot of people are experiencing. I found this that explains how it happens but unfortunately the only way to fix it is to load a save from before either of these situations (I've bolded the one which seems to match your case):

  • If you select a book on a bookshelf and remove it (rather than activating the bookshelf and removing it from the bookshelf's inventory), the bookshelf becomes inaccessible.

  • If you're putting books on the bookshelf and you add one more than it can hold, it puts it back in your inventory along with the message that the bookshelf can't hold any more books. The bookshelf then becomes inaccessible (sometimes the books you were placing on it don't appear, making you lose them books).

Source

PC users might be able to fix this using the console but I'm not really experienced with it.

Hope that helps :)