Well screaming your lungs out in karaoke is probably going to be more helpful for her to let out all the built up stress. Seems like she doesn't have the strength to face someone she considers a peer. Anyone from school, even joo-hyun.
She's terrified to hear what hyun will say even though she knows it will be supportive and kind. Ah-yeong needs an outlet that lets her destress while pretending like nothing happened. Hyun can't provide that since she's in the social sphere yeong is trying to escape from.
I'd say leaving the ice cream on the floor as if it's not there is a pretty good highlight for this. Even just that ice cream is part of her social sphere because it came from hyun. To acknowledge the ice cream is to acknowledge a reality she wishes didn't exist. Also how could she accept hyun's kindness when she so rudely ignored her even though hyun's intentions and actions were filled with care for her.
The self-loathing kicks in and makes you turtle. Unable to accept the kindness of your friends and family. Feeling like you're undeserving of it.
This poor kid