Thanks everyone, ALL of your posts were helpful, reading them helped me confirm my suspicion about the nature of my particular phobia.
I now realize that it is not as big of a deal as I was afraid it might be, with some training I should be able to menage it well. I will probably start with some sort of training/conditioning immediately, try to expose myself to heights more frequently, take small steps (baby steps

).
One more month and I will finally be back in the states, and can take other steps to get myself ready for the Army.