Hi
Welcome to the MedHelp forum!
You need to consult a chest specialist. Did the X-ray show congestion? It can be asthma or allergic bronchitis or even gastric reflux causing the cough.
Tale steam before bed time and an antacid gel and see if it helps until you gte an appointment. Take care!
See PULMONARY specialist...sooner than later. Not only do you have a family history that waves the chest/lung flag, but what you describe, and 2 rounds od antibiotic says to me...time for a lung specialist.