Brahmas are late layers anyway. I don't know if you have a true Ameraucana or an Easter Egger from your spelling, but my Ameraucanas laid about 25-28 weeks but my oldest EE hen laid her first egg at 40 weeks old, so not that unusual for one to lay very late. But, she was not my latest layer. One of my Barred Rock hens from an old heritage line beat her out at 44 weeks for a first egg.
I'm not sure treating them for respiratory illness would affect that-we have a no-treat policy for contagious respiratory illness, but have never encountered any so far in a dozen years of keeping chickens, so I have no experience in that regard and any possible correlation. Maybe someone else could help you with that part of the question.
As far as coccidiosis, that is so common, it probably would not affect laying onset whatsoever.