She must know that the whole country thinks shes be let off lightly so unless she really thinks shes innocent then why would she appeal. Not knowing all the details does make me think that maybe the press aren't focusing on all the story just the shocking parts to sell papers.
Because she's heavily invested in a medical degree and probably wants to complete it. A non-custodial sentence or even some very small odds at trying to get off the conviction entirely is probably a worthwhile punt for her millionaire parents to fund.