It's unlikely to be heartburn. What you're actually feeling is the healing process. "Heartburn"-like pain is how the esophagus communicates pain and discomfort. At this point the swelling is approaching it's peak stage so that sort of pain should be expected. Nexium won't do anything since it's not acid reflux causing the pain. Motrin or other over the counter pain medicine should work just fine if you're now off the narcotic pain medicines your surgeon gave you.
Nissen Fundoplication April 30, 2013
Pain-Free, Reflux-Free, Sleeping on my back!