。
She strongly recommended that I see a doctor.
Literal
She [topic-は] me [to-に] doctor [from-に] examine-receive [as-ように] strongly recommended.
Two grammatical choices to notice. (1) ~ように勧める ('advise/suggest that someone do X') is the indirect-recommendation frame, parallel to ~ように言う ('tell to') and ~ように頼む ('ask to'). (2) すすめる has multiple kanji for distinct senses: 勧める (recommend, urge), 薦める (recommend, endorse a person), 進める (advance, move forward) — all read すすめる. Writing in kana keeps it ambiguous, suitable for general 'recommend.' 強く is the adverbial form of the i-adjective 強い ('strong'), giving 'strongly.'