Not me czy Not I ?

Ona jest spragniona. Nie ja.
She's thirsty. Not I czy Not me ?

Wiem, że gdyby był przykład z have to not me byłoby poprawne np. She has a dog. Not me.

nie widzę róznicy

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I'm not

Technically speaking, the correct answer (as you might have been taught 50/60 years ago) is 'not I', exactly for the reason as shown by the person above - you could alternatively say "I'm not". Saying "me not" would be wrong.
However, English moves on, and English changes over time and uses of English which were not strictly correct have now become OK, so in today's English world, 'not me' and 'not I' are both correct. 'Not I' is however, seen as more 'formal'.