Maybe the story involves some secrets that are not meant to be shared. It could also be that there are some parts of the story that are too personal or embarrassing for Nick.
First, you could try to talk to Nick and see if he is willing to let you tell the story. If he isn't, then just let it go. You might also consider writing the story down for yourself as a way of processing the clue, but without sharing it with others.
This could be due to a bug. Try reloading an earlier save and see if the issue persists. Sometimes glitches happen during gameplay that can disrupt quest progression.
Perhaps in the fanfiction, Judy starts to spend more time with a new character. Nick, who has a deep bond with Judy, sees this new relationship as a threat to their friendship or partnership, and jealousy creeps in. For example, if Judy and the new character are working on a special project together that Nick isn't part of, it could trigger his jealousy.
Maybe it's a bug in the game. Try restarting the game or the relevant level. Sometimes glitches can be fixed simply by refreshing the system.
One reason could be his own clumsiness. Maybe Peter is always in a rush and not paying enough attention to his surroundings. For example, he could be running down the stairs while looking at his phone and trip, resulting in an injury.
One reason could be that she is a strong advocate for the LGBTQ+ community and any story about gay individuals touches her heart as it represents the struggle and beauty of their experiences. Another reason might be that the story has elements of universal themes like love and acceptance, which she deeply relates to regardless of sexual orientation. Also, she may have friends or family who are gay and the story makes her think about their lives.
In some fanfictions, it might be due to political reasons within Hogwarts. For example, if there is a power struggle between different factions, Snape could be seen as a threat or a liability to one side and they find a way to get him fired. His loyalty has always been somewhat in question in the eyes of some, so it could be exploited.
Maybe he was involved in some rough sports. For example, in a game like rugby where there is a lot of physical contact, a wrong move could lead to such an accident.
One possible reason could be that he was framed for a serious offense he didn't commit. Maybe someone planted false evidence of him attacking a fellow student. Another reason might be that he continuously defied the school's strict rules in order to pursue his own goals of getting stronger faster, which the school authorities couldn't tolerate.
Maybe the story contains some sensitive information that Queen Elly doesn't want to be spread widely. For example, it could be about personal family matters or some political secrets that are better left unsaid.