This is the 9940th most frequent Japanese word.
貰っ
"貰っ" is the conjugated form of "貰う," meaning "to receive" or "to get."
貰いました is the past tense of the verb 貰う, which means 'to receive.' It is used here to indicate receiving a physical item, in this case, a book.
私は彼から本を貰いました。
I received a book from him.
助けて貰いました indicates receiving help or assistance. This usage shows gratitude for the action performed by someone.
彼に助けて貰いました。
He helped me out.
読んで貰いたい expresses a desire for receiving the action of someone performing something benefitting you, in this case, the teacher reading the essay.