Wow, have you had her evaluated for RSV
? CJ was very similar as a newborn, turns out when we all went to get out flu shots when he was an infant, he picked up RSV, which is essentially a persistent cold in infants and generally only causes problems with preemies or otherwise immunosuppressed infants. His simply presented as a persistent slew of cold symptoms and a chronic productive cough.
Anyway, it caused me a great deal of grief, though admittedly CJ seemed less bothered by it than I was.