Strategically speaking, this is the most optimal way for a piece of shit prince to get her to the party. Someone would've noticed the brooch outside her dormitory already, and rumors may have already spread of her being the chosen one. That would make it immensely difficult for her to reject the prince.
However, there is a way to counteract this. She has two witnesses, her friend and Riol, that can claim that she was already taken beforehand with a brooch to prove it. It would force her to attend the party, but it would allow her to reject the prince. She would have to be strategic about it, spreading rumors of her already being taken instead of directly confronting the prince to avoid being seen as disrespectful. It would damage the prince's reputation (though it would put her in an unwanted spotlight, especially from the other first years who covet the prince) and it would make it harder for him to approach her later on (though I doubt he would care).
If Sharina took that route, the best case scenario would be the prince confronting her during the party, and her firmly rejecting him in favor of her chosen partner. It would mark the prince as the one in the wrong.
But this comes with repercussions, and her place in the school may be negatively affected. The delusions of the other first years may lead her to being seen as the one disrespecting the royals anyways, despite it being bad manners to pursue someone already taken. Something like it's so romantic for the prince to pursue someone like that, even leaving a brooch because he was too shy to approach her directly. They would just have to hope that people see reason. Otherwise, Sharina might get bullied by the other first years. Hopefully not though.