I always thought I had a fear of heights, but I actually think it is a fear of falling (from a height).
I am completely fine in tall buildings or in a plane, but will not go near the edge if I am on a cliff top, mountain etc. Although if there is a fence/railing then I am ok.
It's bad enough that I feel uncomfortable travelling in a car while driving up a road which has a sheer drop off the edge, to the point I can't/won't look out the window at the view. It seems worse going up, rather than going down the mountain. Strange I know.
As a kid I had a massive tantrum when we had a family trip down to Melbourne and we drove along the great ocean road and went to the 12 apostles. At that time, you could still walk out on one of them (the London Bridge). I cried and screamed and refused to go. My poor dad had to sit with me and wait while the rest of the family walked out on it.
I am happy to say that I did eventually make it down the giant staircase at the Blue Mountains. It took 3 attempts, on 3 different trips out there, but I did it. I don't think I let go of the handrail the entire way down though.
So I guess that would classify as a phobia.....
The other thing I can't bring myself to do is watch someone receive an injection. Pretty ironic considering I am diabetic and inject myself twice a day without issue