It appears that your son has been diagnosed as a case of bronchospasm. Asthalin, Budecort and Deriphyllin are all bronchodilators (i.e. they dilate air passages in the lung).
Asthalin contains salbutamol while Budecort contains budesonide (a steroid). When patients do not respond to salbutamol alone, we need to add a steroid. However one should try to minimise the number of puffs to be taken during a day, particularly in children. Hence it is better to give Aerocort inhaler 2-4 times daily as needed. Aerocort contains salbutamol and beclomethasone (a steroid which is very similar to budesonide). Thus the number of puffs will get reduced by half.
Global guidelines on the treatment of bronchospasm in children do not favour the use of oral theophylline (such as Deriphyllin) due to its low safety margin and side effects. Moreover, one should attempt to control symptoms with specifically targeted medicines such as inhalations that reach the lungs straightaway. Oral medicines reach the lungs after roaming about in the blood throughout the whole body.
If at all three medicines are required, there are better, safer oral agents available such as montelukast (Montair). However symptoms in most children can be controlled by carefully adjusting the dose.