I found a name for the inflammed tongue regarding a B12 deficiency and it is called 'Burning Mouth Syndrome'. If this is what she has, it makes so much sense that she adores those fudgesicles because not only are they yummy but they are wonderfully cold!! And I was thinking about the tub faucet. When I turn my tub faucet on cold, it is sooooo much colder than the sink and develops this condensation on the metal and frost even. I wonder if Puddy is preferring the tub faucet because it may be colder. Maybe she would like some icecubes to lick or a shallow bowl of icewater or since she doesn't 'do' bowls maybe you could put the plug in your sink and put some water in there with a few ice cubes and see if she goes for it.
p.s. and if she is seeking out colder things, she might eat chilled Fancy Feast or other things.