Oops!...I Did It Again - S2-E22
Plot hole: Lily was vomiting because of the antibiotics she was taking for the infected tattoo. But initially, Sean and Claudia were both puzzled by her being sick. As a teenager, how could she have seen a doctor and been prescribed medicine without a parent knowing?
Answer: It happens. One of my middle school/junior high classmates was suspended for fighting another classmate during the weekend, at a location nowhere near the school. Also, after Jimmy and Lily created the fake image of Sister Helen, it's easier for Sister Helen to get away with assigning an unfair detention.