Irrational fears

[rado84]

But my fear of heights is not a problem for normal things at this point.

Try working on a Bulgarian gas station where you must walk on top of a moving (parking) tanker truck (on the semi-trailer, to be precise) to open hatches and valves preparing them for the flow of fuel while the truck parks. If you can do that without falling from the semi-trailer and without having dizziness, I'll declare you an official winner of own fears.  
I don't know what the job of American gas station workers is, but here in Bulgaria we're the ones to climb on top of the truck when it's time to refill the underground tanks.

However, I still wouldn't classify the fear of heights as an irrational fear. It's an integrated problem with one's vestibular system which is more of a health problem than a simple fear.