。
She insisted that I see a doctor.
Literal
She [topic-は] I [subject-が] doctor [from-に] examination receive [as-ように] strongly demanded.
医者に診てもらう ('to see a doctor,' literally 'to have a doctor examine [me]') uses ~てもらう — the verb of receiving a favor — to package medical examinations as a service one receives from the doctor. The に marks the doctor as the source of the action. 強く求める ('to demand strongly') escalates 求める ('to seek, to ask for') with adverbial 強く. 診る ('to examine [medically]') is the medical sense of 見る — written with the radical 言 to mark the technical sense.