Many chickens with a respiratory disease with gaping and swallow as the chick is doing in the video. Head shaking, watery eyes, eye bubbles, and crackles when breathing are other sounds. You said that one had conjunctivitis, and so I would guess this might be mycoplasma gallisepticum or MG. It is a chronic disease, and symptoms can be treated with certain antibiotics. Tylosin, oxytetracycline, Denagard, doxycycline, or enrofloxacin are some that may treat it. Some of those may be found online for pigeons. Testing can be done on your birds, and if you should lose little Bojangles, I would try to get a necropsy done with testing by your state poultry vet. Here is a good article about MG:
https://extension.umd.edu/sites/ext... Mycoplasma gallisepticum (MG) Infecti....pdf
https://extension.umd.edu/sites/ext... Mycoplasma gallisepticum (MG) Infecti....pdf