The universal sign for choking is clutching one's throat.
Coughing can be present when choking, however, it can also be indicative of other problems such as respiratory distress. If the patient is choking, their airway is obstructed usually in such a way that yelling and being vocally disruptive is not a possibility. If the patient is refusing to eat, then they cannot be choking on an object or food bolus; this does not mean refusal to eat is not a problem; it actually means quite the opposite, deserving investigation as to why the patient is refusing to eat.