You might want to give an introductory ride a try. Often being afraid of heights doesn't translate into a cockpit. I hate going up on a ladder but I'm perfectly comfortable in an aircraft, even small helecopters with the bubble canopy.
Make sure you do it with an understanding instructor however and make sure he or she knows so they can bring the plane back if you do panic. There seems to be a difference between fear of flying and fear of heights. Some pilots are shakey looking off a tall building while perfectly comfortable at 30,000 ft while high steel workers can be terrified of just being in an airplane sitting on the ground.
Just take it slow and easy until you know how you react.
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