This cough even lasting for 4 weeks needs to be looked into other causes. Pin prick like spots on wrist may be due to small petechial rash
which some times associated with vigorous cough usually in whooping cough
and your child cough is more in the nights as you told may be due to underlying bronchospasm
also so better you consult your Pediatrician
again for follow up and explain the series of your child complaints and he will assess your child problems and advise accordingly.