Your son has typical symptoms of allergic asthma
and combination of bronchodilators (such as budesonide
inhaler with spacer device), montelukast
4mg, antihistamines and steroid nasal sprays (used for 6 weeks and stopped before restart after 3 months) is the standard management plan.
As with all steroid usage, growth retardation is a recognised side effect but much lower than oral steroids
as inhaled steroids are generally used to control airway inflammation along with montelukast.
Skin prick testing is recommended to ensure common household allergens like cats and dog dander are not making the asthma worse when avoidance will be key. House dust mite allergy
is also important to know as changing bedding or adding a layer of protection with dust-proof covers for mattress, pillows, duvets are important. Important to get rid of old soft toys as they accumulate dust very quickly.
I hope that was useful.