Caroline Banana, of Bentilee, further admitted making a false representation on an Income Support application form by not declaring she was owed her TV gameshow winnings, in April 2011.
She also pleaded guilty to wrongly claiming free school meals for three children.
She now has 12 months to settle her over-payments in full.
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Paramedics had to take the boy to a hospital 18 miles away from his home following the closure of a local children's A&E.