I fear heights and flights

Dear doctor; I have an acute fear of heights. When on the second floor of a building, I cannot look down without my getting dizzy. These are avoidable, but the real problem comes when I have to fly. The whole idea that a plane ‘floats in space’ keeps my heart thudding throughout a flight. Sadly, it is next to impossible for me to sleep during a flight. Are there some drugs that I can use to fall asleep to avoid such scenarios? Can these fears be medically related in some way so that it can be treated?
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Times Reporter