I don't want to scare you... what I'm about to share is absolutely the worst-case scenario.
My first bird, Ruffles, had similar but not identical symptoms. Her difficulty breathing came on very slowly. She also had increasing difficulty with pooping.
At the time we lived in the middle of nowhere and the only vet in town didn't have much experience with birds. Also, my family didn't have much money so she didn't even get her to this dog/cat vet until way too late. We were sent home with antibiotics.
I was in the 8th grade and spent all my free time caring for her, making sure she got her medicine at the right times. It got to the point where she couldn't poop without being over warm humidifier air. Then she stopped being able to poop entirely. Within hours her breathing was so labored that my mom sat me down and explained that it was becoming cruel to try and keep her alive. We took her back to the vet and that became one of the saddest days of my life.
They did an autopsy and she had an ovarian tumor the size of a hard-boiled chicken egg yolk. I think the vet was trying to be comforting when he told me that I must have been taking incredibly good care of her because he had never heard of a tumor that size in a cockatiel. She was more then 10 years old at the time (another major difference!).
I hope with all my heart that your story has a different ending then mine. You're already very much on the better path. I understand how hard it is when a little one suffers... Our hugs to you and your family.