Penguina,
The inner ear senses accelerations. The three semi-circular canals are at right angles to each other, and therefore can detect accelerations in all three axes, and the brain can resolve these signals into a resultant direction of the acceleration. However, as soon as the acceleration stops, regardless of how fast you're going, the fluids in the canals run back to the lowest part of the canal, and so you don't feel the speed. the system is not particularly sensitive, as aeromed people can demonstrate with a 'spin chair'. You sit in a pivoted office chair with a blindfold on and the chair is very gently spun, with a very slow acceleration. This 'sub-threshold acceleration' is not quick enough to displace the fluid from its resting position so you think you're not moving. Once they've got the chair spinning quickly they suddenly stop it. The fluid sloshes violently in the other direction under the deceleration. Your brain, having not known you were moving before, interprets this as a violent acceleration in the opposite direction. So to sum up, they spin the chair to the right; you think you're stationary. They stop it quickly; you are convinced you're spinning rapidly to the left. They tell you to take the blindfold off-you fall over!
As an aside, an aeromed guy once told me that one of the reasons you get dizzy when drunk is that these fluids are quite thick. Alcohol gets into them and thins them out, so they slosh around more. So your inner ear tells your brain you're moving much more than your eyes tell your brain. Result: motion sickness!
In response to your crosswind question, the crosswind doesn't create an acceleration, so I don't think you would feel it. You would sense a powerful sideways gust, though.