。
She's afraid she might fall ill again.
Literal
She [topic-は] again sick become [might-not-it-be-のではないかと] is-fearing.
~のではないかと expresses tentative fear or worry about something — literally 'thinking isn't it the case that X.' The のではない frames a hesitant double-negative ('isn't it not the case'), and the closing と quotes the worry as the content of 恐れている ('is fearing'). The whole frame is how Japanese softens an apprehension into something less than a flat claim. 病気になる ('become sick') uses ~になる for the state-change of falling into illness, treating it as a transition rather than a sudden event.