Allium cepa, or red onion, is a homeopathic remedy for (surprise!) runny noses with burning in the eyes. The nasal discharge tends to be acrid and makes the skin around the nostrils raw, while the tears are bland and soothing.
This is a good example of the homeopathic principle: The symptoms a substance causes in large doses (stinging eyes, runny nose) can be cured by small doses of that same substance. In homeopathy, this is called the Law of Similars, otherwise expressed as "Similia similibus curantur," or "Let like cure like."
When we refer to small doses, of course, we're talking about homeopathic doses, which are nano-doses of the original substance, usually starting at about one part in a trillion. The homeopathic process (grinding, diluting and succussing, diluting and succussing, etc.) is also important to making a homeopathic doses more effective.
Allium cepa is useful not just when someone has been chopping onion but also, for example, in colds with acrid nasal discharge or for seasonal allergies. People who need Allium cepa generally feel worse in a warm room and much better outside.
Strangely, it is one of our best remedies for the intense neuralgic pains of amputation and for heel blisters.