I feel your pain, OP.
Our neighbours had one. It crowed ALL day. Unbelievably loud - it sounded like it was perched on my sill whilst the window was open.
I was working 12 hour nightshifts in the NHS at that time so was getting no sleep. I tried earplugs but after three consecutive ear infections I gave up. They didn't work anyway.
I was so worn out I had to take time off on the sick as I felt I was going to make the kind of mistake that could hurt or kill a patient. My commute was a 40 minute drive each way and I was finding myself nodding off at the wheel.
Unfortunately, it was the middle of the summer so the bloody thing was crowing 18 hours a day from 4am and I still wasn't catching up on any sleep. (Their barking dogs were also a problem but at least they only started at 8am. Went on til 11pm, though, but that's another story.)
I was so tired I felt depressed to the point of suicide - or murder.
I spoke to a locum GP about anti-depressants and explained why I was so depressed and he got in touch with the local council for me. They served a notice, birds were removed by the owners and peace was somewhat restored. I recovered and was back at work in a few weeks.
I really hope you get the bird or birds removed (my neighbour actually had 3 cocks so no wonder it was so noisy. Who the hell needs one let alone that many!). People who can sleep through anything are very lucky and have no right to make light of this kind of situation. There's a reason sleep deprivation is used as a method of torture - it works!
Councils should make noise nuisance a priority. It's awful for people who have to live with it, whatever the source. I'm still prone to bouts of depression since it kicked off with this and I feel truly sorry for people who suffer with hyperacusis.
Good luck.