Get some foam earplugs if it bothers you that much. My husband raised pigeons for years . They are universally called squeakers as babies. Guess why? They squeak. When they get older they are called Squab which is a whole other subject.

I think you've been listening to that bird too long and it's repetitiveness has been stuck into your brain. You've tried ignoring it for so long but worried about the bird that your brain thinks that it's still making a sound.

I found a baby pigeon abandoned on my balcony last week. So my parents and i am taking care of it. It squeaks a lot since we keep it inside because our neighbour has a big cat and we keep it safe inside, however at night or day when i goto my room and lay down i hear the squeaking in my head...though its not squeaking. I have great hearing however i think because in always hearing the bird squeaking it stuck in my head a a bit. How about you do you think so?