'Nor' is grammatically correct as it involves negation...i.e. includes 'not/didn't' or ' neither.' Generally, in America, though, a lot of people would just use 'or' here in general speech or casual written exchanges we're pretty lax on these things. Only a grammar stickler would notice it, in the US at least. Using 'nor' results in the statement sounding more deliberate or emphasizing the point, to me anyway.