The only thing I can think of that should cause that is string or something on the ground, though I think I would probably see that, at least in your second picture. You haven't been playing around with structure blocks or anything have you?
I'd agree, try building it somewhere else though that shouldn't really matter.
As a matter of fact, NOTHING in the outer ring of the 5X5 area around the enchanting table interferes with the bookshelves there. Only things in the 3X3 ring just outside the enchanting table block the bookshelves.
The left table in my screenshot gives a level 16 enchantment, just like the right one.
What do you mean by "I can't get to do enchantments over level 14..."
Post a screenshot of what the actual enchant window looks like when you put an item in there. I.e. an iron shovel.
My setup in this world has exactly 15 shelves. You can see third row showing lvl 30. But as I have no lapis in there, they are all greyed out.
You saying your third row only shows lvl 14?
My second image is from creative with only 7 shelves, that gives me 14 on the third row,
Clear everything out. Table, shelves, all.
Prep a nice 5x5 platform that does not involve dirt/grass. Put table in center. Check enchant levels it gives you, especially 3rd row. Start placing bookshelves on the perimeter one by one, and checking your enchant levels after each placed shelf. If you place a shelf, and levels don't change something is wrong with that placement.