This is a bit of a stretch, as it it won't kill everyone very quickly, but is close to your criteria (natural substances, antiA fixes A but exacerbates B). If you're okay with some very broad strokes and yada-yada-just-believable-enough attitude toward it, then you might be able to sneak by with this.
Really, any metal poisoning will do for our purposes, it's just that arsenic has been around and used for millennia. Arsenic is a naturally occurring metal. Long-term exposure can lead to serious health issues and complications. A large enough quantity in the short term can be used as a poison.
Copper would also work as a metal poisoning. Again, really any metal poisoning will do for this situation.
Antidote for Metal Poisoning: Penicillamine
Penicillamine is derived from penicillin, which has a long history - penicillin is naturally found in molds, and even ancient Egypt, Greece, and India have documented histories of using fungi for the treatment of certain conditions. Although whether or not they were using those from the penicillin family is unknown, the penicillium family of bacteria are naturally occurring. Fermentation processes go back to ancient Egypt, so someone with know-how in a D&D universe could certainly ferment certain fungi to get penicillamine.
Penicillamine is used in metal poisonings. It's not a fun medication to take. Vomiting, diarrhea, etc. But in an emergency situation, if someone was poisoned with large amounts of copper or arsenic, they might prefer this to death. It's not an "antidote" per-se, but it will indeed treat the metal poisoning.
A single wasp sting is unlikely to kill you (unless you have a serious allergy), but just like metal poisoning - if someone were to extract enough into a consolidated substance, it would indeed kill you. Not that quickly, but probably painfully. For our purposes we'll focus on one aspect of wasp venom - it's interaction with kidneys.
Penicillamine <=> Wasp Interaction
There are no known cases of penicillamine interacting with wasp venom. I don't think anyone would dare try it. But penicillamine has a long list of bad drug interactions. It's not the thing you shove down your throat for kicks and giggles.
Note that penicillamine also has very toxic reactions to renal and liver diseases. In other words, if your kidneys aren't functioning well, penicillamine will have a drastically exacerbating effect on the harm to your kidneys, which could be fatal.
Because wasp venom, in enough of a quantity, will get into and cause damage to your kidneys (pretty quickly too), then penicillamine will have a drastically exacerbating effect on this. While penicillamine is making you puke and pee out metals, this dehydration and impact on your kidneys could probably knock you unconscious pretty quickly, and kill you shortly thereafter.
It's not the "instant" death you're looking for, and I don't foresee any scientific research being done into the interactions between wasp venom and penicillamine, but if you're okay with some broad strokes and yada-yada-ing over details, then maybe this will work for you.