No,nebulizer therapy won't help here. The basic problem is due to reflux,specially while lying down,leading to irritation of throat,leading to cough. Feed the baby at a gap of atleast 3 to 3-1/2 hours,avoid top milk feeds,but if forced to,use katori and spoon to give feeds. Do NOT wake him up for feeds. Burp him for atleast 10 mins after every feed,then lay him down on HIS right side for half an hour after burping. Keep him elevated by placing a cushion beneath the head and shoulders,24/7. This usually helps,but if it doesn't work even after following religiously for a week,consult again. Meds have a limited role,and may be used as a last resort.

Keep the head end elevated after feeds. Ensure burping after each feed. You can give Domstal drops for symptomic relief. If the reflux is hampering the normal growth of child then he needs to be evaluated by a specialist.