The doctor also told me that it's not an ear problem, but rather a brain problem. The brain is supposed to filter out this noise, in the same sense that it filters out the sounds from a (normal) digestion, our breathing, etc. I do have some (undiagnosed) hypersensitivity, so that sounds consistent to me.
nozzlegear: it gets better with time, the less you think about it. I know it's not a great consolation, but trust me, train yourself not to think about it, and it will go away for extended periods of time (and will come back from time to time)