Like literally everyone but the MC, I find these meds super suspicious. The temple is keeping tabs on her specifically, considering her marriage more important than even the duke's marriage. She is the descendant of a powerful light user with some crazy prophecy, and they've been feeding her pills from the age when magic manifests until now. The temple isn't even supposed to deal in medicine, from what the duke says, so why would they know how to handle some esoteric disease that only she has, and personally handle the supply of pills?
The weirdest thing here is that she, a reincarnated person, would not find anything strange about the situation. I mean, the original was brought up being told that she has to eat them, and would not think twice about it as something "she's always done", but the MC should have been a bit more curious about what exactly this deadly disease she had is (which literally killed her already), and what the pills do, and possibly how to get them from some other source since apparently she doesn't even know who the contact supplying them is. If she loses that bottle, would she even know how to get another on short notice? Would she just walk up to the local temple (a month's travel away from her home town's, so it's not like anyone there would know her) and be like "hey, the temple back home has been providing me with these white pills my whole life, but I lost my current bottle and need a refill within the week or I die. No, I don't know what they're called, what they're made of, or what they do".