Regarding 8-month old, fever & cough needs evaluation as doctors need History, examination (&maybe tests)to confirm diagnosis & manage condition. If there was this issue from day1 age, then urgently consult.
Regarding 4yr old boy, with coughing on exertion, it might be exercise-induced asthma: so needs assessment by Pediatrician
Next Steps
Consult pediatrician, as your details cannot be accessed online