"...do you remember people getting sick a lot?"

"Not around me.  I think in other places not everyone can afford the right crystals."

"Do you know what they do in places where there are not magic crystals?"

"...Do you mean, where people can't afford the right ones, or do you mean like here where maybe you don't have any, because instead you have real monsters?"

Haru breaks back into English in exasperation. "Here what we do is vaccines, I mean what do you remember people doing in Flatland where they could not afford magic crystals."

"Ummm.  I think they just get sick.  They might die, I suppose, if it were bad enough.  I know that some people came to Verona for the affordable healing."

"Well, here what we do is vaccines. Crystals aren't magic unless they happen to come from a dungeon that does magic crystals. And everyone has to get vaccines so you don't get sick and don't get other people sick. If you don't get vaccinated with dead - or it might actually just be weakened? - Japanese encephalitis virus, then instead the first way Japanese encephalitis virus will get under your skin is from a mosquito bite and then it will be completely alive and your brain will swell up. Etcetera etcetera for all the other diseases there are."

"A what?  - A what bite?" she clarifies.

"...a mosquito." He pulls up a picture. "They suck blood, and carry diseases."

"That seems really bad..."

"It is! It's really bad! And there are diseases that spread other ways too but the one I remember having to get vaccinated about specifically to come here is a mosquito one."

"I am glad you have a way to deal with your awful problems here, but I don't think that will work on me."

"We can tell the doctor that we aren't sure if you might be a monster," says Ren, "and if there is some way the doctor can tell, then that's that, we don't give nonhumans human vaccines. But if it isn't obvious to a doctor then I won't be able to get a note excusing you from being vaccinated for school."

"..........Okay, Swan-san."

"Are you ready to go or do you want the bathroom or anything first?"

"Umm, yes."  And she will take the opportunity to stall and compose herself against whatever might happen next, for a minute.

But then they can go.

They go by train! Ren does her best to give a rundown of what a normal checkup without any magical crystals might be.

None of the other components sound nearly as alarming.

Ren accompanies her into the hospital where she is getting her checkup. "Normally we would go to a smaller clinic," she says. "But because this is a strange case you're being seen here instead, the same place where you saw the esper."

They don't have a long wait. The doctor introduces himself as Kodera-sensei and he can speak English, though he, too, often resorts to Jisho.

Kennedy has a growing sense of unease about how - medical, this place looks, now that she's here to have diseases stabbed into her body instead of to be magically evaluated.  She greets Kodera-sensei with careful politeness and hopes he doesn't notice how nervous she is.

Before anyone stabs any diseases into her body, he wants to do "all the quick and obvious tests" - this involves removing some blood, which Ren is careful to explain does not insert anything lastingly into her person, and listening to her heart and looking into her ears and throat and checking her reflexes and suchlike.

....Okay, they can take a little of her blood, once they establish to her that it's only a little.  Ears throat reflexes are all normal; her heartbeat is - pretty elevated, is the main thing notable about it.

Also it's maybe in a weird place? He'd kind of like an X-ray but if that freaks her out too, getting started on vaccines is the priority. She's got some bespoke blood type but the blood is otherwise blood.

She's doing her level best to appear not freaked out.  "Kodera-sensei, I do not think a vaccine will be good for me."

"No child likes them," he tells her. "That is normal to not like them."