Three months of white mucus in the throat with cough on exertion and at night is not an infection any more - two courses of antibiotics have already proved that. This pattern is usually post-nasal drip from allergic rhinitis or sinusitis, and often there is a cough-variant asthma or acid reflux component on top. What helps: a daily steroid nasal spray (fluticasone/mometasone, two sprays each nostril, used for at least 4-6 weeks), saline nasal wash twice a day, montelukast with levocetirizine at night, and avoiding late heavy dinners. Because she gets cough specifically on walking fast, she needs a chest X-ray and spirometry (PFT) to rule out asthma or COPD rather than more antibiotics.
Next Steps
Stop further antibiotics, start the nasal spray plus saline washes, and get a chest X-ray with spirometry done. Bring the reports to a Practo consult with me or to Synergy Multispeciality Hospital, Miraj; if she coughs blood, loses weight or gets breathless at rest, she needs to be seen the same day.