There is no shame in seeking professional help if you believe you have a true phobia. According to psychologist Rich Presta, the reason anxiety disorders are diagnosed more often in women than men is that men are reluctant to acknowledge anxiety---to themselves as well as to others.
Learn about air safety, how aircraft work, and the incident statistics of the airline on which you will be traveling. Although fears are rarely rational, this information may help you to recognize your fear as unfounded and counter it with facts.
On the plane, practice deep breathing exercises if you feel your anxiety becoming overwhelming. The physiological symptoms of fear---including rapid heartbeat, sweating and dizziness---can themselves contribute to your fear, so it is important to keep them under control while you remind yourself of the reality and safety of your situation.