This is post-viral airway inflammation with sticky secretions - the cold has settled but the mucus in the chest is thick, so it feels stuck. Montelukast alone will not clear it; what helps is good hydration, steam twice a day, and a mucolytic like acetylcysteine or ambroxol plus deep breathing and huffing to bring the phlegm up. At 50, if you smoke, that is what is keeping it there.
Next Steps
Start steam and plenty of warm fluids today; if the cough is still there after a week, get a chest X-ray and CBC. Fever, breathlessness or blood in sputum means see a doctor the same day. Consult me on Practo with your current medicines and I will give you the exact regime to clear the chest.