For how long he is having this cold
and nose block?
Infection in nose and sinuses
causes block in nose. Discharge from sinuses and nose that is phlegm (mucus) flowing back to throat irritates his voice box causing him to cough.
You can use saline nasal drops to nose. This makes the secretions in nose thin and allowing them to flow back, there by helping to open up the nose.
He may need a course of antibiotic to overcome the infection.
Once the infection is controlled he is likely to take feeds better.
You please show him to a GP/paediatrician/ENT specialist