Passively dampening sound is done by carefully combining solid, flexible, and porous materials to change the frequency and volume of the sound. Airplane sounds operate on a wide range of frequencies. Removal of the low frequency bands will be difficult, because they actually move the entire structure; so don't expect a lot from adding a new, hard-surface wall. Attenuating the high-frequency turbine scream has been a problem for the engine designers; they've been required to do the best they can.
Consult designers of theaters and recording studios. The materials they use are designed to eliminate the sounds that annoy you. The porous tile wall and ceiling covering, along with thick rugs absorb sound. I did suggest that design of a bed with a sound-attenuating half-cover, similar to the principle of the street phone booth, is less expensive than a whole room.
You need also be concerned with codes for egress during fire. A sound-proofed sliding panel, similar to a closet sliding door, may be a solution for covering the window portion of your thickened or added wall.