Translation:I am the second girl.
Fata...no? We use the definitive...or no?
No. In expressions like "the Nth <noun>", the definite article is actually expressed by the ordinal numeral, so there is no article used by the noun. See this thread for more info.
Why isn't it 'doilea' ?
Because this is for masculine nouns.
Eu sunt al doilea băiet.
Couldn't this also be translated as "I am the second daughter."?