I've been a nurse and worked with kids in hospitals and this isn't all that uncommon. Your child sounds like he might have "reactive airway disease." It's not a "disease" but a non-specific term for "asthma" and a few other respiratory problems. Many small children experiencing symptoms are classified as having asthma but some doctors term it reactive airway disease at this stage as the child is still young and not every wheezing attack is asthma. There is specific criteria for asthma and some kids eventually outgrow this phase. Not all children who wheeze have asthma and many children under three years who wheeze are not predisposed to asthma.
Basically, as adults, we can fight infection and deal with the common cold/RSV. Small children have a hard time with infections because of the fact that their immune systems are not fully developed yet. Breastfeeding helps because mom's antibodies become some of the baby's antibodies so the baby can fight infection much better.
Also, as adults, we have large airways. Little children have tiny airways and that causes a lot of problems for them. When a bacteria or virus or even an allergen enters a body, the body tries to fight it with inflamation of the airways, mucus production and sometimes hyperresponsiveness of the airways (the muscle around the airways constrict). This slight narrowing of airways in adults usually isn't a problem as we start off with large airways but with kids, this slight narrowing closes most of their airways. Kids with this present with respiratory distress ranging from mild to severe shortness of breath, wheezing, cough, the snuffles and fever.
Many times, children have a common cold and then develop the asthmatic symptoms. Often, the cold is precipitating trigger for their symptoms.
So your child may or may not be asthmatic. Time will tell. If there is a specific trigger, you'll find it eventually. Hope this helps. And remember, don't take what I have written here as perfect, please talk about this with your pediatrician
