If it's an illness, they could search for a cure. Maybe there's a special herb or a magic spell in the world of the fanfic that can heal her. Her friends could go on a quest to find this cure, and in the process, there could be more character development and interesting plot twists.
Since I don't know the exact 'the screaming woman story', it's difficult to say. But usually, the screaming woman herself would be a main character. There might also be someone who hears her screams, like a passer - by or a neighbor.
She might be a character representing the general state of women in a particular society or situation. Maybe she's a symbol for all those who are oppressed and are finally finding their voice to scream out in protest.
Often, there could be the person who discovers the screaming skull. Maybe it's a curious explorer or someone who moves into an old, supposedly haunted house.
Dan Brown's 'The Da Vinci Code' has a lot of mystery elements. With all the secrets about the Holy Grail and the ancient codes, it keeps the readers in suspense and there are many moments that can make you feel like screaming in surprise as new revelations are made.
Some characters might immediately rush to her aid. Harry and Ron, for instance, would be very concerned and would do everything they could to figure out what was wrong and protect her from whatever was causing her distress.
There might be some sort of misunderstanding or prank in the story. For example, someone told the kid that Santa isn't real as a joke, and the kid is so distraught that they start screaming. Christmas is often a time of high emotions, and for a child, something like that could be very upsetting.