Praise be to Allaah.
If the medicine containing alcohol is essentially an intoxicant, such that drinking a large amount of it would make one drunk, then it is haraam to take it or to give it, because the Prophet SAWS (peace and blessings of Allaah be upon him) said: "Whatever makes one drunk in large amounts, a little of it is haraam" (Reported by the four muhadditheen and others; see also Saheeh al-Jaami’, no. 5530). If it is not an intoxicant, then it is permitted to give it and to apply it to the skin, etc.
And Allaah knows best.
Sheikh Muhammed Salih Al-Munajjid