But now it's time to focus. She's thought of some important things that she wants to do before she heads back, this time. She was honestly planning to try to talk Inuyasha up to staying for both Thursday and Friday, but he's being really really decent about helping her get here in time for her math test, and even gotten her an entire extra half-day, so she's going to use it, and be ready to go when she said she would be. She gives her grandfather a hug (he's the only one home, since it's the middle of the day), tells him she'll be home again for dinner, and then she rushes off.
First thing's first: filter masks. The home improvement store has those fairly heavy-duty half-face masks that people use for working around paint fumes. Kagome doesn't have a lot of money - this'll pretty much wipe out what she's saved from birthdays and occasional chores - but she's gonna buy two anyway. Two demons with poison gas powers in the space of one week is enough that she suspects the toad won't be the last.
Second thing: drug store. Turns out you can't buy oral antibiotics over the counter, which is... fair... but really inconvenient, given that she'll feel really bad if Nobunaga does get a serious infection and die of it. She's not sure what to do about that. "Just give up" seems like a really bad and cowardly thing to do, but she can't think of a reasonable way to get a prescription, and she definitely doesn't want to try to steal medicine, so she's kind of stuck. She mills around for a bit and ends up buying some extra bandages, some topical antibiotics (which are for infected wounds, right?), and an extra bottle of ibuprofen.
Third thing: the library.
The Shikon jewel is considered to be a legend. But legends do get written about, or at least remembered, even if nobody believes in them; that's what makes them legends in the first place. So if the Shikon jewel is a legend, then it ought to have something written about it, somewhere. And if, in the past, it shattered and caused a ton of trouble for lots of people, there ought to be something written about that, too. And maybe, just maybe, some of those writings will be so kind as to include regions, or specific varieties of demon involved, or even something about her (although she's not sure whether she's dreading that or not).
By bothering the librarian repeatedly and flipping through books that are old enough that she needs a dictionary to fully make sense of them, she's able to determine that her theory is... partly true. There are mentions of the Shikon jewel as a mystical artifact said to grant the wish of whoever possessed it. There are not mentions of anybody shattering it, or of the shattering causing any problems, at least not that she can find. Which is very weird? You'd expect this sort of thing to leave some ripple in the stories people told, if it really did cause all the problems that it seems like it would cause.
Maybe time has to wind itself up in particular directions, when it bends the rules and lets you go back in time at all. Maybe it has to keep you from catching a glimpse of your future self in the mirror of the past. It wouldn't be the weirdest thing she's seen this week (which is honestly probably still the pocket dimension inside Inuyasha's eye). But it bugs her.
She heads home late, and arrives in the middle of dinner. Hugs her sister and her nephew. Regales people with an edited-to-be-less-horrible-and-terrifying version of the stories of Sesshomaru and Tetsusaiga and the toad spirit (and Ayako still seems pretty horrified, but at least she also seems impressed and approving). She asks her grandfather whether he knows any stories about the Shikon jewel being shattered. He doesn't. Sota has a pile of new homework for her, which she slips into her bag and then cheerfully resolves to ignore until tomorrow.
By evening she's really too tired to study, but she feels a responsibility - she's not really sure to who, maybe to herself and maybe to her parents and maybe to Inuyasha, of all people, for giving her the chance - to at least try to do well on the test, so she still takes a halfhearted stab at it before going to sleep.