Hay, I feel you, ang frustrating talaga ng recurring cough lalo na pag multiple xrays na pero clear, kaya third opinion is totally valid! A few of us mums went through similar with our kids at honestly, mas nakakamahusay kung may doctor na makakita ng pattern ng symptoms, kaya I'd recommend asking around your pedia or sa online mom groups here for specific pedia-pulmo recommendations sa both hospitals, word of mouth talaga ang best way para malaman kung sino ang thorough at nakikinig talaga. Since may allergic rhinitis history pa, pwede rin yang triggering factor kaya mas important na may doctor na holistic ang approach. Definitely try both hospitals at compare kung paano sila nag-assess; trust your gut kung saan ka mas comfortable at confident na may solusyon!