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According to one source Nila or Nyla is a feminine version of male names Neil and Niall. But since you are not referring to the middle-eastern part of Ireland, a more plausible explanation would be that your name is related to the river Nile :)
Early references river Nile and its God, "Neilos", are found in Hesiod's Theogony. According to some sources, "Neilos" may have originated from the Semitic root *nahal*, meaning a valley or river valley.