It's not a horribly sad situation. They are acting well enough I think, their lives seem pretty full and rewarding, they jump and fly and run. They aren't lying about not feeling well, though we all know how they don't show it until they are really sick. It's just how they sound. Maybe I can get a video with sound.
Well I am of the opinion that like us Hoomans our animals will get sick, have injuries and have to heal and get better on their own mostly.
I only intervene if they have a heavy respiratory illness and high fever, nasal discharge, etc. then I give antibiotics, the same deal that you did with you wee kiddie.
In addition to that I am a firm believer in pain meds; if a person or animal is in pain then they will not be eating or sleeping properly which puts additional a stress on them, Red Hen is an example, she is old I am sue she has a heart condition, likely cancer, but I can keep her comfortable, and as long as she is eating I am happy to let her enjoy her life.
As for testing for whatever illlness there might be, that risk of A. Influenza will be a risk; flocks with this show sever onset of illness and morbidity is around +90% if you flock tests, positive every bird will be culled. And every other flock around yours may also be culled.
For this reason alone I would never bring my bird that was ill to a Vet for testing. And I try to keep a low profile with my birds, I don’t advertise I have a flock here. My horse Vet knows of my flock and that’s it.