Fanfiction.net is also a good place. Just use the search bar and type in key words related to the scenario, like 'nico', 'percy' and 'crying'. There are likely to be some stories there.
One possible fanfiction could be 'The Unseen Pain'. In this story, Percy might be crying due to the overwhelming pressure of his demigod duties. Nico stumbles upon him in a secluded corner of Camp Half - Blood. Nico, initially hesitant, decides to approach Percy and offer his silent support.
I don't think it's a very common or popular theme. The Percy Jackson fandom usually focuses more on positive relationships and adventures among the characters. Choking is a rather dark and extreme concept that doesn't really fit the general tone of the fandom most of the time.
Perhaps he's feeling guilty about something that happened during one of his quests. Maybe he made a decision that had negative consequences for someone he cares about, and that's weighing on him. It could also be that he's just had a really tough encounter with a powerful enemy and is letting out the pent - up stress and fear through crying.
Well, in some versions, Percy might be initially shocked. He could be like 'Whoa, I had no idea!'. Then he might start to see Nico in a new light, with more understanding and compassion.
Nico might be initially shocked. He could feel a deep sense of anger towards whoever was responsible for Percy's abuse. Then he would probably become very protective of Percy, vowing to keep him safe from any further harm.
The 'enemies - to - lovers' trope is often used in these fanfictions. When Draco finds Harry crying, it can be a turning point in their relationship from animosity to something more. For example, in some fics, Draco's initial shock at seeing Harry vulnerable softens his feelings towards him over time.
I'm not sure where you can specifically find a fanfiction with that exact plot. You could try popular fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. Just search for relevant tags like 'Percy', 'Nico', and 'Will' to see if such a story exists.
One possible plot development could be Nico seeking justice for Percy. He might start to investigate the abuse on his own and gather evidence against the abuser.
The camp leaders might betray them. If there is a power struggle within the camp, and Percy and Nico are seen as threats to the current leadership's power, the leaders could set them up. They could make it look like Percy and Nico are breaking camp rules or endangering the other campers, which would lead to the rest of the camp turning against them.
There could be a fanfiction named 'A Moment of Vulnerability'. In this, Lily finds Snape crying in the Potions classroom after a particularly harsh encounter with James Potter. It shows how Snape's pride is broken and Lily's reaction to seeing his vulnerability.