Postnasal drip refers to the sensation of mucous flowing from the back of your nose down to your throat. This results in an inflamed voice box causing it to be hypersensitive. A hypersensitive voicebox can result in a persistent irritative cough that can last for weeks to months. The two most common reason for a postnasal drip are Allergic Rhinitis (Sensitive nose aka Hayfever) and Sinusitis (infection of the sinuses). To treat your postnasal drip, it is important to treat the underlying cause.
Patients with Allergic Rhinitis experiences frequent blocked nose, runny nose (usually clear), sneezing, nasal itch, watery eyes and postnasal drip. Diagnosis is achieved from a combination of clinical history, physical examination including a nasoendoscopy (a relatively painless scope through the nose under local anaesthesia) and an allergy test (most often a skin prick test). Treatment of allergic rhinitis includes allergen avoidance and the use of nasal steroid sprays and oral antihistamines/decongestants. Immunotherapy (desenstisization to an allergen) is an option for patients with a known inhalant allergy who wish to explore a potential cure for allergic rhinitis.
Patients with Sinusitis typically presents with blocked nose, facial pain, coloured nasal discharge (yellow, brown, green or blood-stained), postnasal drip and decreased or loss of sense of smell. Diagnosis is achieved from a combination of clinical history and physical examination, including a nasoendoscopy (mucopus may be seen in the drainage pathway of the sinuses or the nasal cavity). Treatment of sinusitis usually involves a course of oral antibiotics, nasal wash with saline water and nasal steroid sprays.
Sometimes the feeling of a "postnasal drip" may be due to an inflamed voicebox from acid reflux from the stomach. Since you have a persistent postnasal drip that is causing an irritative cough that is affecting your partner, I would strongly recommend a visit to an ENT Specialist for an assessment.
Hope this helps and all the best!