In fanfiction, Percy could throw up because of intense emotional stress. Think about it, if he's faced with a situation where he might lose his friends or family, the anxiety could be so overwhelming that it affects his physical state. He might also be exposed to some kind of dark magic that has a negative impact on his body. And sometimes, fanfiction writers like to put their characters through really tough physical challenges, like running for days without rest, which could lead to exhaustion and vomiting.
Perhaps it's due to the interference of the gods. The other deities might not approve of their relationship for various reasons. Maybe Zeus, fearing the power that could come from a union between Percy and Artemis, decides to put an end to it. In the world of Percy Jackson, the gods often meddle in the affairs of mortals and demigods, so this could be a factor.
Perhaps he has been exposed to some sort of deadly and unknown substance in the mythical world. This could be a new type of monster venom or a strange plant that he accidentally ingested. The substance could be attacking his body from the inside, causing his internal organs to bleed, and thus he throws up blood.
It could also be due to a sense of guilt. If something bad happened that he blames himself for, like someone getting hurt because of him, he might exile himself as a form of self - punishment. He'd rather be alone and deal with his own pain than face those he feels he's let down.
One reason could be that Percy is loyal to Annabeth. In the original series, his relationship with Annabeth is strong, and he might not want to betray that for Artemis. Artemis is also a virgin goddess, which adds a layer of complexity to any potential relationship.
One reason could be that he's interested in different mythologies. Percy Jackson is full of Greek mythology elements, and Harry might want to explore how other fictional works handle such themes. Another reason could be for pure entertainment. Fanfictions often offer unique takes on existing universes, and he might find the creative interpretations in Percy Jackson fanfictions engaging.
Maybe he feels guilty. Suppose he made a big mistake, like accidentally leading an enemy to a safe haven of demigods. The guilt could be so overwhelming that he exiles himself to punish himself and keep others safe from his potential future blunders.
One possible reason could be a misunderstanding. Maybe Artemis misinterprets Percy's actions as being against her or her hunters. For example, if Percy accidentally endangers one of her hunters during a quest, Artemis might see it as a betrayal of her trust in him.
One reason could be Percy's more fluid connection to his powers. Since he's been using his water - based powers for a long time, he's more in tune with them compared to Jason. So in a power - based showdown, Percy would have an upper hand.
Well, in fanfiction, one reason could be the loss of his friends. Percy has been through so many battles, and if he loses someone close like Annabeth or Grover, it could send him into a deep depression. Another reason might be the burden of his prophecies. He's constantly expected to save the world, and that kind of pressure can wear a person down over time.
In some fanfictions, Percy might be banished because he goes against the traditional ways of the demigod society too much. For example, if he tries to form an alliance with a group that the other demigods consider enemies. His actions could be seen as a threat to the stability of their world, so they banish him to keep the peace.