It is most likely that your daughter has asthma. You have a strong
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Family troubles - resources history of asthma and allergy. Also she has had repeated episodes of breathing problems. In fact, an asthma attack looks exactly like pneumonia when the x-ray is taken when the airways are closed. It is probable that this episode was also an asthma attack. Skin testing is not really needed to make this diagnosis or to start
preventivePreventive health care therapy. I would talk with your doctor about this. It may be necessary to refer your daughter to a pediatric pulmonologist or board certified pediatric allergist. These two specialists deal with children your daughter's age all the time. It is not likely that either will do skin tests. It is more likely that a program to get these symptoms under control and prevent the next attack will be started.
The most common medicines used for the symptoms are inhaled beta agonists to open the airways. There are a variety of medicines that might be tried for prevention, depending on what they feel at the time of the examination.