yes your son has very high chances of getting asthma
, the medication given by the doctor is also correct i advice you to follow the doctors advice and give the medication properly,there are chances that he may not develop asthma. also you improve his general health, which will again reduce the chances of getting asthma.
i also suggest you get a skin prick test done for him by an immunologist, then you will come to know if he is allergic to something which is causing asthma. if he is strongly allergic to something then immunotherapy
can be started which actually has potential to cure asthma to some extent.
also with correct medication asthma can be controlled very well.