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.
What is meant by travelling, according to the Muslim scholars, is to go or move from a place of residence to another place covering a distance equal to 83 Km or more. This is the travel considered in many rules regarding shortening the prayers, breaking the fast and similar issues. However, the Sharee’ah rules that apply to a traveler are terminated by the traveler’s return to his home or his intention to staying more than four days in a given place. This is the opinion of the majority of the Muslim scholars.
So, any travelling person who intends to remain somewhere for more than four days he is no longer considered a traveler. So, all rulings related to travelling do no longer apply to him. Since your brother accompanied you during your trip and as long as the place where you dwell is secure and the people with whom you live are peaceful, then if these conditions are met, your brother does not have to stay with you because you are no longer travelling and it is the travel that requires a Mahram.
Moreover, the lawfulness of studying abroad is restricted to being able to study in a safe environment where the woman does not uncover herself or get mixed with non-Mahram men as this might lead to bad consequences.
Allah knows best.