This could be because of postnasal drip since you complain of nasal block.
Next Steps
first stop coughing forcefully, it only worsens the irritation. use nasal decongestant drops like Otrivin 2 drops thrice daily for 5 days. continue steam inhalation and tab Montek LC. if you have acidity or reflux you continue veloz d too. salt water gargling twice a day.
Health Tips
take plenty of fluids, avoid exposure to cold, stop clearing your throat.