Hello!
So I won a giveway for a game for the E-Shop and it didn't work. So I thought that the code was sent from NA and I'm Eu.
My question is if NA codes only work on NA e-shop, and if the answer is yes I would like to know if there is something I can do to change that.
Thanks in advance.

well even if they worked outside Nintendo's region lock would make it impossible for you to play with a non-NA console... so yeah they only work in NA

as for a solution you could contact whoever/whichever company gave you the code saying you're not from that region to see if they can solve your problem.