How do you know if a 3 months old son is suffering from asthma?

Consider other cause. 3 months of age is very young for asthma. Usually parents think this because baby is coughing or has noisy breathing. At 3 months the usual causes are bronchiolitis or gastroesophageal reflux. Less commonly there may be a congenital problem like laryngotracheomalacia, a vascular ring, or a cyst in a large airway. Clearly your infant may need to be seen by a pediatric allergist or pulmonologist.
Need evaluation. There are many different reasons for a 3 month old to have difficult breathing. Asthma is just one cause but you need to be concerned about others. It is important that he be evaluated to make sure none of the of the other reasons are the cause.