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Alcohol has little place in children's medicine, or in their lives in general.
The biggest concern we have in young infants and children is the danger of serious hypoglycemia (low blood sugar). This occurs in one of two ways. The most common cause of dangerous hypoglycemia is the "morning-after" syndrome. There has been a party, and there are many half-consumed alcoholic drinks sitting on the coffee table. These are sweet, and get tasted by an early rising toddler. The toddler is discovered later, mysteriously unconscious. On evaluation in the emergency room, the astute ER doctor gets the history of the party, and draws blood tests that show a very low blood sugar and a high alcohol level. A sugar infusion is curative, but extremely low blood sugar can potentially cause brain damage. BAD.
The other situation, thankfully rare, is that ignorant parents have rubbed a young baby with alcohol for fever control. This should never be done for anyone, young or old. It is unnecessary and again, potentially very dangerous. Use acetaminophen or ibuprofen for fever - not alcohol rubs!
The amount of alcohol in over-the-counter medications is generally harmless, and not a great cause for concern. It is less prevalent than it used to be, as well, for many companies have removed it from their medications because of the general bad press alcohol receives, not because of any real danger in the amount of alcohol in the medicines.
Alcohol does pass in breast milk, but not in amounts that would generally be harmful unless the mother were really drunk. A glass of wine in the evening to help the letdown has long been prescribed with nary a report of problems. I am unaware of any reports of hypoglycemia in a nursing baby because the mother had a very high blood alcohol level.
(I will leave the entire discussion of teen drinking and how parental modelling has a lot to do with it to other venues for now.)