The literature from wine makers suggests that there are at least three possible causes of medicine flavored wine - a high alcohol, low acid wine; brett contamination; and the use of chlorinated water.
If, however, the problem is the high alcohol, low acid wine then I cannot get my head around why simply adding acid would not solve the problem. The advice given by those who suggest that that is the cause is to dump the wine... so I am skeptical about that reason. If the origin is from brett contamination or from the chlorophenols produced in the presence of chlorine or chloramine then I cannot see how aging will solve the problem... but prevention in the first place would.
As for the need for a kit to measure TA , I am not sure that one is needed. The color change point always takes place at a pH of precisely 8.2 so if you have a pH meter, and some sodium hydroxide and something to measure the volume of sodium hydroxide that you are adding to the wine to the point where the pH of the sample measures 8.2 then you are home and dry.