Unfortunately, but you cannot just link a new Nintendo Network ID (NNID) to your Club Nintendo account to re-download your game, as any digital games you previously downloaded are locked to the original NNID, sorry.
So if you are unable to relog in with your original NNID, perhaps the best thing to do is give a call to Nintendo's 1-800-255-3700 (6 am ~ 7 pm Pacific, everyday) Customer Service number, or use their webform to contact them, and one of the service representatives can find out what the problem is, or in some other way make it so you don't lose your copy of Pokémon Y.
