Is it a sin for a girl not to drink or eat from utensils that someone else has touched before her, including members of her family, and is she sinful for refraining from using her parents’ cups?

It was part of the Prophet's guidance (peace and blessings be upon him) to avoid pretentiousness. He would drink from the same spot where Aisha (may Allah be pleased with her) drank, even when she was menstruating, as narrated by Muslim. It is advisable to abandon such pretentiousness, especially if it causes others' feelings towards you to change. There is no sin upon you, Allah willing, as long as this is a natural disposition and not arrogance.