The SI reflexive particle is used when she chose it for herself. She chose the field of her studies for herself to study. Had she chosen it for her son, it would be KTERÝ OBOR MU VYBRALA.
And no JSI is "You are" and not the same as "SI", though they sound the same and many many Czechs, sadly, would write JSI believing that SI is colloquial. So do not feel too bad.
The term "field" or "field of study" is broader than "major". The term "major" is used at many U.S. colleges and universities to indicate the coursework that an undergraduate specilaizes in. However, a doctoral candidtae (Ph.D.) would not be said to have a "major". He/she would have a field or field of study.