Hi, the possible causes of cough with sputum are Gastroesophageal reflux, Laryngopharyngeal reflux, Respiratory tract infection, chronic bronchitis, Bronchiectasis etc. You need to undergo lungs radiograph, endoscopy to rule out the causes. You can go for centrally acting cough suppressants, mucolytics and steam inhalation after
Consultation from physician, as well as appropriate therapy is essential.
You need to undergo lungs radiograph to rule out chronic bronchitis, Spirometry for lung function tests. You may be allergic pollens which may be reason for the allergy. In such cases try avoiding exposure to the allergens.
You need to send the sputum or throat swab for culture, microscopy, staining to rule out the pathogen and should also take chest radiograph. If there is infection you need antibiotics course and proper rest for some days with healthy food like fruits vegetables etc .Take care and regards.
Sounds like allergies. You should see a doctor for an accurate diagnosis and recommendations for treatment.