Cough after the upper or lower respiratory tract
infection is not an uncommon thing.It is called post viral cough
, which is dry and is severe at night.It can last for 4- 6weeks and steam inhalation along with cough suppressants can help.
Worrying part is the lose of weight, I think you need to be checked for tuberculosis
with symptoms of cough and weight loss
Please do not just start taking some medication in hope of increasing weight, try to have the proper investigations first to rule out a more serious problem.