I think you can't say for sure from this sentence. As is discussed in the notes for this lesson, if it were "flegistino", you could say that it was a woman for sure, but the word "flegisto" can be used either for a man or as a general term that does not distinguish between male and female. In the latter case, the nurse could here still be a woman.
You're asking for help here, so you need imperative (a plea is a some sort of command: Help me, do it!)
Using the infinitive (the i form of the verb) would be like saying "Nurse, to help me", which does not make much sense.
Alternatively, one could say something like "He'd like to help me", which would be "Li ŝatus helpi min". Or "I'd like to be helped", "mi ŝatus esti helpata".
Does that help?