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.
Grover would be panicked. He's Percy's friend and he cares a great deal about him. He might start running around trying to find help, like looking for a healer or someone with magical healing abilities. He'd probably be muttering to himself about how he should have protected Percy better.
Well, it could be due to some sort of magical potion gone wrong. Maybe he drank something that was supposed to give him extra strength but instead made his stomach turn. Another reason could be that he got poisoned during a battle with a monster. Some monsters might have venom or toxins that could make him sick to his stomach.
It could be related to a new and strange power he's trying to control. Percy is constantly evolving and getting new powers. If he tries to tap into a power that his body isn't ready for, it might have some adverse physical effects like vomiting. Like when he first started to understand his water - based powers, there could be something similar but more extreme with a new power.
It can create a sense of urgency. If Percy throws up, it might mean he's been poisoned or is seriously ill, and his friends will have to find a way to help him quickly. This can drive the plot forward as they search for a cure or a way to make him better.
Try this one: 'Are you a demigod? Because you've got the power to make my heart race faster than a satyr at a party.' Satyrs in the series are known for their energetic and wild nature, so comparing the effect the person has on your heart to a satyr's energy is a fun way to flirt. It also ties in the concept of demigods which is central to the Percy Jackson world.
It could be a rogue demigod who wants the throwing stars for their power. This demigod might have been shunned by the other demigods and sees the stars as a way to gain revenge and power over them.