For what it's worth, I could be mistaken. The storebought deionized water I get could be contaminated with carbonic acid, which would explain the burning.
Distilled water tends to exhibit an acidic because there are nk dissolved salts to buffer against atomspheric carbon dioxide which forms carbonic acid once dissolved. However I would be very surprised if store bought water contains enough CO2 to irritate human skin, unless you meant carbolic acid instead of carbonic acid.