Hello,
Thanks for posting your query.
Persistent cough with blocked nose is indicative of infection in the airways.
The impacted phelgem needs systemic antibiotics to deal with. You will have to consult your physician to get the best antibiotic and brochodilators prescribed for you. Steroids- both oral and inhalers might be needed for symptomatic relief.

However the best treatment for impacted mucus is steam inhalation. Inhaling steam from a bowl of hot (but not boiling water) may help to soften, and loosen, the buildup of mucus in your nose. You may also find that adding some menthol crystals, or eucalyptus oil, to the water helps a lot. Other than that, avoid eating indigestible, spicy, foods and meats and eat simple wholesome foods. Out-of-door exercise, sunbaths also help a lot.
If you have fever or the cough is worsening then it is advisable to get a X-ray chest done to rule out pneumonia as well.
Meanwhile you can follow the following remedies:
1. Stay hydrated. Fluids can help reduce the dryness of the airway and help symptoms
2. Inhale steam thrice daily.
3. Elevate your head with pillows at night to ease a chronic dry cough.
4. Do not smoke or use tobacco product.
5. Avoid inhaling irritants such as smoke, dust, or other pollutants.
6. Ginger and balsam (tulsi) used in tea, also reduces dry cough.
7. Avoid hot and spicy foods
Any over the counter cough suppressants are not likely to help you much. Taking proper antibiotics after consulting your physician will help in early relief.
Hope this answers your query. I will be glad to answer the follow up queries that you have.
Please accept my answer in case you do not have further queries.
Wishing you good health.
Regards.
Dr. Rakhi Tayal.

---