She might use her superpowers accidentally during a school sport event, like making the basketball she throws fly all the way across the field and into the neighboring town.
Well, she could meet a young villain - a student who has some sort of power - in the school. This student might be jealous of Captain Marvel's fame and power. They could start a mini - power struggle within the school grounds. Captain Marvel would have to use her wits and powers carefully to stop the situation from getting out of hand without causing too much damage to the school.
In the 'Captain Marvel goes to school fanfic', perhaps she has trouble fitting in at first. She's used to outer space battles, but now she has to deal with high school cliques. For example, the popular kids might be a bit intimidated by her and the nerds might be overly eager to be her friend because of her superpowers. She could also struggle with normal school subjects like math and history, having been out of touch with Earth's educational system for so long.