Selene wanted Eros to go to the hospital but he refused. His wound was not that serious. Besides, it was just a fake wound of his fake human body. He could fix it if Selene was not there.
But now that Selene had seen his wound, he couldn't do anything about it. He would let his hand bleed like a human since he was pretending to be a human.
But he didn't want to go to the hospital since he might encounter lots of grim reapers there. The hospital was the place where most humans were dying so grim reapers were just around the area, collecting human souls to guide them in the netherworld.
Though they might not notice him, Eros was still cautious not to be found out by grim reapers. He was also avoiding seeing and meeting the grim reaper who might collect Samantha's soul.
In the end, Selene just brought Eros to the Anderson Family Mansion to treat his wound. She could use the first aid kit at home.
