This brings to mind the story of Joseph Smith when he was a young boy, even before he received his first vision. 
 
He had a really bad infection in his leg bone that needed an operation. The doctor offered him alcohol as an anestethic before commencing the operation. Joseph refused, instead he promised that if his father would hold him, he would keep still while the doctor cut open his leg to remove the infected pieces of bone. 
 
If I were in your situation, I would let my doctor know my beliefs regarding alcohol and ask whether there are other suitable non-alcoholic remedies. 
 
I believe if you show obedience to the Lord's commandments, he will help you find the relief that you seek.

If it was taken under the strictest of adhearance to a legal written perscription (which means the doctor wrote it up on a federally reported and regulated perscription note) than you might have an arguemnt.  
 
A doctor recommending alocohol though is not a perscription, it is a doctor giving no medial advice based upon his personal beleifes. I would inform the physican that such a remidy is 1) not legal to recommend 2) unsafe to recommned 3) against my personal views.  
 
I would also consider reproting the physican to the state because the State needs to know about physicans that are "recommending" alcohol as a medininal treatement so they can revoke there license to practice medincine.