Praise be to Allah.
It is not permissible for anyone who does not have wudoo’ (whether they are menstruating or otherwise) to touch the Mus-haf according to the majority of scholars, because the Prophet (peace and blessings of Allaah be upon him) said: “No one should touch the Mus-haf except one who is in a state of purity.” Narrated by Maalik in al-Muwatta’, 468; classed as saheeh by al-Albaani in Irwa’ al-Ghaleel, 122.
A menstruating woman may recite Qur’aan without touching the Mus-haf, according to the most correct view, such as if she recites what she has memorized, or if she holds the Mus-haf with a cloth and the like. She may also read from a Qur’aan that includes commentary, as is explained in the answer to question no. 2564, 60213.
You should have avoided touching the Mus-haf directly, and held it with something that would have formed a barrier, such as a clean cloth, or worn gloves, or turned the pages with a stick or pen and the like.
However, something forbidden took place. All you have to do is ask forgiveness of Allaah and repent to Him. We ask Allaah to forgive you, and we ask Him to accept your good deed and reward you for helping your sister.
And Allaah knows best.