。
She asked me whether I might not be feeling well.
Literal
She [topic-は] me [to-に] feeling [subject-が] not very good [tentative-のではないか] [quotative-と] asked.
A nicely layered hedging construction. The pattern ~のではないか ('isn't it the case that X? / might it be that X?') turns a flat statement into a tentative suspicion — softening 'you don't feel well' into 'might you not be feeling well.' あまり~ない ('not very') further softens the negative into a hedged 'not particularly good.' Combined with the formal verb 尋ねる ('inquire'), the whole sentence reads as carefully indirect — typical of polite, considerate speech in Japanese, where direct questions about another's state can feel intrusive.