“Asian flush” tends to be associated with far more than just a simple facial reddening, and I included the genetic aspect in my response because sensitivity to alcohol can be caused by several things in addition to medication. But yes, medication can and does produce a similar effect to not having the breakdown enzyme by blocking it’s action in those who do have it:
As described here: Disulfiram - Wikipedia)
Disulfiram works by inhibiting the enzyme acetaldehyde dehydrogenase, causing many of the effects of a hangover to be felt immediately following alcohol consumption. Disulfiram plus alcohol, even small amounts, produces flushing, throbbing in the head and neck, a throbbing headache, respiratory difficulty, nausea, copious vomiting, sweating, thirst, chest pain, palpitation, dyspnea, hyperventilation, fast heart rate, low blood pressure, fainting, marked uneasiness, weakness, vertigo, blurred vision, and confusion.
No one person is likely to experience everything in that list of symptoms, but there is enough diversity among people that at least a few might experience just the sweating symptom in response to vinegar when something is preventing acetaldehyde breakdown in their body (I myself experienced that plus headache, and none of the others).
Vinegar is created by converting ethanol (the alcohol that we drink) to acetic acid. As such, there are traces of alcohol in vinegar; enough so that it’s listed as one of several foods to avoid when you are on antabuse drugs.
As I said, it’s a long shot that is what’s happening in the OP’s case but still a possibility.