Not sure why -we did nothing for my birthday- should not be acceptable?
I keep on seeing 'no...nada' as 'not ...anything'. But 'nada' means 'nothing' on its own, so could you say just: 'hicimos nada ...' for 'we did nothing'?
Spanish doesn't have rules against double negatives as we do in English. In fact, I think that the no is required. Hicimos nada would be incorrect. No hicimos nada means "we did nothing" or we didn't do anything."
Spanish does have rules against double negatives, if you research this topic the first thing you will notice is that Spanish negates verbs differently from English, only the negative particle before the verb is the one that negates it, any other negative particle you add after that only reinforces the negative. For example:
- No hicimos nada para mi cumpleaños (No negates the verb, its only purpose is to make the statement negative, and nada acts as a reinforcer, whilst also being the object).
But if you switch the order to put emphasis on nada, it would look like this:
- Nada hicimos para mi cumpleaños (Nada negates the verb, but it's also the object, so no other negatives are required).
If you said "Nada no hicimos" instead, that would be a double negative, therefore grammatically incorrect.
Also DL lists 'anything' as possible meaning of nada. I think that is precisely for these situations.