This is not an easy question and certainly might be answered in different ways by different specialists. Here is one opinion. With the history you are presenting it is likely, rather than a small chance, that this is indeed asthma. It may also be complicated by a chronic sinus condition. This is often silent, but looks like a cold before getting chest involvement. While allergy may play a role, with the history of prematurity, this is probably not a
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With respect to testing for asthma, this is not an easy procedure. It certainly is not done in the office of a primary care physician or a pediatrician. Lung function tests, even in 2-year-old children, can be performed in a special lab run by pediatric pulmonologists, usually in a university setting. We do this frequently here at National Jewish Medical and Research Center.
Pulmicort Respules™ (budesonide inhalation suspension) is a fairly safe inhaled steroid that is easily administered by nebulizer. If there is a suspicion of asthma in a 2 year old, it is not uncommon to begin a trial of this over a period of months. In the correct dose, the risks are fairly low and far less than having one of these significant breathing problems you have described. You cannot try this medicine for a few days or give it on and off. That will gain nothing for your son.
If questions persist, a consultation with a pediatric pulmonologist might help ease your mind. However, it appears your son’s doctor is on the right track.
When I was little I had cancer and was always very sick and my parents said it helped out greartly keeping me in an airconditioned room during the summer months.