Based on your symptoms and the normal chest X-ray and Pulmonary Function Test, the problem is unlikely to be from the lungs. The pattern you described strongly suggests irritation from the upper airway rather than a pulmonary disease.
The most common causes for these symptoms are Postnasal Drip Syndrome and Allergic Rhinitis. In postnasal drip, mucus from the nose and sinuses slowly drips toward the throat causing throat irritation, a constant urge to cough, and the sensation of something stuck in the throat. The small bumps you see at the back of the throat are often due to lymphoid tissue enlargement from chronic irritation, medically called cobblestoning.
The fact that cough is mostly during the day and minimal at night also supports an upper airway cause rather than asthma or lung disease.
Next Steps
It would be reasonable to consult an ENT specialist. They may perform Nasal Endoscopy to examine the nasal passages, sinus openings, and back of the throat to confirm whether postnasal drip or allergic inflammation is present.
Treatment usually includes antihistamines such as Fexofenadine, nasal steroid sprays like Fluticasone, and saline nasal rinses to reduce mucus and inflammation.
If symptoms persist beyond a few weeks despite treatment, doctors sometimes also evaluate for Gastroesophageal Reflux Disease because reflux can irritate the throat and produce similar symptoms.
Health Tips
Stay well hydrated because thin mucus drains more easily.
Avoid frequent throat clearing, as it can worsen throat irritation.
Steam inhalation once or twice daily may help loosen mucus.
Try to reduce exposure to dust, smoke, perfumes, or other allergy triggers.
If you want, you can book an online consultation and share a clear photo of the back of your throat and your full medication history so I can guide you more precisely on whether this is postnasal drip, allergy, or reflux-related throat irritation.