At 4 months old, any sign of reduced feeding and irritability alongside coughing is something I would not sit on, the risk of waiting and things getting worse outweighs the inconvenience of a hospital trip. I would bring him to KKH A&E or your nearest hospital now rather than wait to see if he improves, because babies this young can go downhill faster than we expect. Better to get him checked and be told all is fine, than to hold back and regret it.