Coughing and being sick (way TMI, not for while eating breakfast!) - long, sorry.

[ShrinkingViolet]

I'm not sure whether I'm tipping over into over-protective mothering here, so I'd appreciate some sensible MN advice.
DD1 (14) had a nasty cough, bringing up yellow then green mucus. So we went ot the doctor, got some ABs, mucus went back to pale yellow/clear, but the cough didn't stop. So after a week we went back to the doctor who said the cough (which by now is a huge long thing with gasping for breath at the end, finishing off with being sick, mainly mouthfuls of mucus, but with some food as well). Doctor said the cough was the body's reaction ot the earlier infection, and the sick was a by product of the cough.
Fast forward another week, and she still has the cough (not nearly so frequently, maybe 4-5 times a day), but she's still being sick. Probably retching and bringign up mucus with some food rather than being sick is a better discription.
She's not "ill", no temperature, no "droopiness", no wanting to miss school, and I'm 99.9% sure it's not a food issue, as the retching is pretty uncontrollable.
So, do I go back to the doctor with her, as it's only got a bit better, adn i'm not happy about the gasping for breath (even though they've checked the lungs and she doesn't fit any of the other asthma symptoms), or do I leave it a bit longer, as the doctor said it would get better by itself (which it is, just very slowly).
WWMND?

I feel sick when i cough - i have a strong gag reflex, as does my son. As soon as he has any hint of a cold he starts being sick. It could just be as she is coughing bringing stuff up (the last few bits of infection, its hitting the back of her throat and making her gag and then be sick.

I honestly wouldn't worry, but i don't know the full extent of the cough i guess, so if she is still hacking in say a week, take her back.