。
She went to America to study medicine.
Literal
She [topic-は] medical-science [object-を] study [for-ために] America [to-に] crossed-over.
渡る ('cross over, traverse') for international travel paints the journey as a deliberate crossing — water, distance, threshold. The compound 渡米 ('cross to America') is a fixed Sino-Japanese verb in newspaper register; here the longer アメリカに渡る gives the same flavor in everyday Japanese. 学ぶ ('learn, study') is more book-and-tradition than the broader 勉強する; pairing 医学を学ぶ ('study medical science') gives the sentence a respectful, studious tone fitting a biographical retelling.