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.
Toge Inumaki is important too. His special cursed speech ability makes him stand out. Also, the principal of the school, Masamichi Yaga, is likely to be important as he is in a position of authority and has an influence on Gojo and the other students. There could be other characters like the members of different clans that also play roles in the complex web of the story.
The reason the cartoon kid is screaming might be that they are playing a game and got really excited. Another possibility is that they are in a dangerous situation and are trying to call for help.