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Question: Assalamu alikum brother I forgot to mention in my previous question that I was instructed by the doctor to apply only 2mg solution on my scalp daily which is a very less quantity and alcohol is an inactive ingredient of the medicine so please answer my question whether I can use it or not. May allah bless u for ur work
You are allowed to apply the lotion or solution prescribed by your physician. There is no need to worry for two reasons: You are using it externally and not consuming it. Eminent scholars have ruled that it is allowed to use cosmetics with a small percentage of alcohol. Secondly, the alcohol in most of the medicines has undergone a chemical transformation in such a way that it has been turned into a new product altogether and its original properties are almost non-existent. 
For further details, let me cite here from one of my earlier answers:
If the alcohol - added to it as a medium has been wholly transformed in such a way that it does not result in intoxication, it is permissible to use such medicines.  This ruling is based on the principle of Istihalah which states if a particular substance has been wholly transformed chemically in such a way that the original quality or property in it (because of which it  was forbidden in the first place) does not remain intact, then it is considered as lawful. An example for this is alcohol turned into vinegar; alcohol is haram and forbidden while vinegar is not.


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