What should I do, as I have falsely sworn upon the Quran, and is there expiation upon me?

If you forgot when you swore that your sister had not made you swear to something, then there is no expiation (kaffarah) or sin upon you, because it is considered a 'laghw al-yameen' (a futile or unintentional oath) which is pardoned. However, if you swore falsely and you were not forgetful, then this is an 'yameen ghamus' (a perjurious oath), and there is no expiation for it according to the majority of scholars. However, it entails a great sin and repentance is obligatory for it.