One idea could be that Artemis becomes mortal to understand Percy's human world better. Maybe she's intrigued by his heroism and wants to experience life from his perspective. This could lead to a whole new set of adventures as she struggles with mortal limitations.
There could be a love story. Artemis, now mortal, might develop feelings for Percy that she couldn't as a goddess. This would be a complex relationship as Percy already has his own life and relationships. The fanfiction could explore how they navigate these new emotions.
In this type of fanfiction, it could be a really interesting concept. Percy becoming a god already changes the whole dynamic of the Percy Jackson universe. And marrying Artemis, who is a virgin goddess in the original mythology, would be a huge deviation. It might lead to a story full of challenges as they have to deal with the reactions of other gods and goddesses. Maybe Percy's new - found godly powers would help him navigate the complex relationship with Artemis, who is known for her independence.
You can try Archive of Our Own (AO3). It has a large collection of fanfictions, including many about Percy and Artemis in the mortal context. Just use the search function and type in relevant keywords.
In this fanfiction, Percy becoming a god and marrying Artemis could mean a complete overhaul of the power structure in the mythological world. Artemis might teach Percy more about the secrets of the divine world, especially those related to nature and the hunt. Their union could also bring about a change in how mortals view the gods. Maybe mortals would start to see the gods as more approachable and relatable, especially with Percy being a former mortal himself. And Percy would have to deal with the fact that he is now part of the divine family, which comes with its own set of politics and expectations.
Well, there's 'Percy's Mortal Adventure with Artemis'. This fanfiction takes the idea of Percy being mortal and throws him into a series of challenges with Artemis. It's full of action and the relationship between the two characters is explored in a unique way. There are some really cool fight scenes and the story keeps you on your toes throughout.
Percy could also react with a sense of determination. Instead of being defeated by the injury, he sees it as a challenge. He starts to figure out what made Artemis hurt him in the first place. If it was a misunderstanding, he tries to clear it up. If it was something more malicious, he starts to plot his revenge. He uses his own wits and the powers he has to either heal himself or find a way to make Artemis see the error of her ways. He might also seek the help of his friends, like Annabeth or Grover, to come up with a plan to deal with the situation.
The Hunters of Artemis are very likely to show up. They are Artemis's loyal followers and would surely be involved in the search for their mistress. Annabeth could also be there. She's Percy's friend and has great wisdom, which could be useful in devising a plan to save Artemis. Grover might be another character. His ability to sense things could help in tracking Artemis or finding clues about her whereabouts.