How do I work through my aviophobia?

I am dreadfully afraid of flying and it results in rather physical reactions to it during flight. I know it is a completely irrational fear when you are given all the statistics and safety requirements but I simply can not get it out of my head that I am in an enormously heavy metal object in the air. I suppose my fear is more concerned with the actual functioning of the aircraft rather than the possibility of terrorist threats. I feel very well protected by the TSA. I have exhausted all possible resources on the internet to help cope with this fear and have found little comfort. I'm going on a flight from Los Angeles to Zurich this summer and would really like to start working towards being okay on that flight. Should I simply take sleeping pills or should I speak to my doctor about a more appropriate method of subduing my anxiety? Any helpful tips from fellow flyers would be greatly appreciated.