Is what I did a sin, and what should I do to atone for it? Do I have to re-recite the pages I recited while not in a state of purity? If so, must I inform my teacher so she can re-recite them for me, or can I re-recite them for my mother?

As long as you were not certain that menstrual blood had descended, what you did—continuing to read and keeping the Mushaf—was correct. This is because merely feeling the symptoms of menstruation, or doubting the descent of an impediment, is null and void and holds no weight unless you are certain. This is based on the Prophet's (peace and blessings be upon him) saying: "If one of you finds something in his belly and is unsure whether something has come out of him or not, he should not leave the mosque until he hears a sound or perceives a smell." You are not required to repeat what you read, nor to inform the teacher.