The predominant symptom of bronchitis is cough and that of asthma is breathlessness. Your daughter is having cough when she exerts herself leading to vomiting and breathlessness which is an evidence of her pulmonary function being less than normal. Asthma is the insufficient exchange of gases in the lungs and bronchitis like condtion keep intervening.
Homeopathic medicine has good remedies to get rid of the cold, cough and breathlessness due to exposure to cold or due to allergies. As the time moves on with treatment there would be an improvement of
dr.Venugopal gouri.

It's probably normal when she is sick.. Some people are more susceptible to getting congestion in their lungs when they get a cold. I'm about the same. However, when she exercises there is a thing called "exercised induced asthma". Basically it's asthma that flares up only when you are exerting yourself pretty hard such as running around. It may be wise to mention it to the doctor so they can give her an inhaler when she wants to exercise. I have a mild form of it myself.. Especially in colder weather.. If I try to run or do harder exercising my lungs feel like they tighten up and I start coughing and have trouble catching my breathe. I always just treated it by taking lots of breaks and not exercising too hard.