Well, he might be unable to perform his duties on the ship for a while. His friends would surely be worried sick and would probably do everything they could to nurse him back to health. Maybe Annabeth would take charge of his care, using her wisdom to find the best way to heal him.
It could be an enemy that manages to sneak onto the Argo 2. Maybe a monster that they thought they had defeated before but actually just bided its time and then attacked Percy when he was least expecting it.
She might be unable to perform her normal duties on the ship. For example, if she's in charge of some magic - related tasks, her injury could disrupt the magical balance or protection on the Argo 2.
He could have to take a long time to recover, which might make him feel frustrated and impatient. It could also lead to him doubting his abilities as an Auror for a while.
They might face new and strange monsters. For example, they could encounter a sea - serpent that has the power to control the weather around the Argo 2. Percy would use his water - controlling abilities to try and fend it off while Annabeth comes up with a strategic plan to defeat it.
Maybe he's missing his family. He's been away from them for a long time on the Argo 2, and homesickness could hit hard and make him cry.
Percy's performance in future hunts could be affected. Mentally hurt, he may make more mistakes due to lack of confidence or focus. Physically hurt, his skills may decline until he fully recovers. His overall attitude towards the hunt could also turn negative, which would not only impact him but also those around him in the hunt fanfiction.
He might not be able to spread as much joy. If Jack is hurt, his powers could be weakened. So, the children in his area may start to feel less happy and more afraid, as his presence and ability to create positive wintery magic is reduced.
In many Percy Jackson fanfictions where he gets hurt, it often leads to his friends rallying around him. For example, Annabeth might use her wisdom to find a way to heal him quickly. His demigod powers could also play a role in his recovery, like his connection to water might help soothe his wounds if they're burns or something related to fire. It's a common trope to show his vulnerability and the strength of the bonds he has with others in these situations.
Maybe in the fanfiction, if someone on the Argo 2 endangered his friends, Percy would get angry. He's very protective of his friends, like Annabeth. If any harm came their way because of someone's recklessness on the ship, that could set him off.
Well, it could be about Percy and Annabeth having some sweet, romantic moments on the Argo 2. Maybe they're sharing secrets, or just enjoying the journey together while facing some minor challenges on the ship.