All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We would like to advise you, dear questioner, not to shave your head because it is either disliked or prohibited for a woman to shave her head according to the jurists.
The Hanbali scholar Al-Mirdawi said in Al-Insaf: “It is disliked for a woman to shave her head without any valid excuse according to the correct view of the school of Fiqh. It was said that it is forbidden.” [End of quote]
Moreover, Kashshaf Al-Qina‘ (a Hanbali book) reads: “It is disliked for a woman to shave her head or cut her hair without excuse because it was narrated by Al-Khallal with its chain of narrators on the authority of Qatadah that ‘Ikrimah said: “The Prophet, sallallahu ‘alayhi wa sallam, prohibited that a woman shaves her head." If there is an excuse like ulcers, then it is not disliked.” [End of quote]
Moreover, Ibn Abu Zayd Al-Qayrawani said in his book Ar-Risalah: “The act of Sunnah is shortening the hair for women, and it is not permissible for women to shave their heads.” [End of quote]
The prohibition is further emphasized in your case, as long as shaving your hair would incur your mother’s anger, as you mentioned. It was authentically reported that the Prophet, sallallahu ‘alayhi wa sallam, said: “The pleasure of the Lord lies in (i.e., is earned by attaining) the pleasure of the parents, and the displeasure of the Lord lies in (incurring) the displeasure of the parents.” [At-Tirmithi] [Ibn Hibban and Al-Hakim: authentic]
Preoccupation with studies is not a valid excuse to deem it permissible for a woman to shave her head and incur her parents’ anger, and the oily secretions produced by the scalp that you mentioned may often be treated with medications if it is proven to be a health problem and not a normal matter. In brief, you should not shave your head without a necessity or need, for treatment purposes, for instance, and stay away from what incurs your parents’ anger, may Allah, The Exalted, grant you success.
Allah knows best.