The internal pressure of your body is accustomed to air pressure where you live. At the altitude that airplanes travel, the pressure is much lower than your internal body pressure. Should the pressure on the outside of your body be reduced, one of the first signs of this problem would be a nosebleed.
You do experience small changes in pressure while flying, and these cause your ears to “pop.” This occurs because the inner ear pressure presses your eardrum outward. When the pressure on both sides of the eardrum equalizes, your ears pop. Swallowing helps to equalize this pressure.