。
She's started looking older all of a sudden.
Literal
She [topic-は] suddenly grew-old [becoming-てきた].
老け込む is a compound verb formed from 老ける ('to age, to grow old in appearance') plus 込む ('go deeply into / become deeply in a state'). 込む is one of Japan's most productive auxiliary stems — see also 信じ込む ('be utterly convinced'), 落ち込む ('sink into depression'), 教え込む ('drill thoroughly into someone') — and it pushes 老ける from neutral aging into a more dramatic 'visibly aged, looking notably older.' The ~てくる auxiliary on top adds the sense of a change unfolding toward the present, framing the aging as an emerging trend rather than a fait accompli. 急に ('suddenly') is the everyday counterpart to the more formal 急速に.