The first weeks are the most challenging. Yes, often the sensation of "heartburn" is actually an irritated esophagus that interprets the pain as heartburn.
I don't know if your doc told you, but your wrap becomes increasingly swollen for the first two weeks, so don't be surprised if your swallowing gets more difficult. Once past the two week mark, things begin to calm down and you're on your way.
Are you taking pain meds at night? Although you won't need them much during the day, it is worth taking them at night so you can get some sleep. If you can get your rest you can tolerate a lot more of everything!
I'm glad you've joined us, Sirkit! Welcome to what we post Nissen members call the "Wrapped Club"! You're a full-fledged member now! Please post your recovery progress and if you have any other worries or concerns, post away! We'll do our best to answer your questions and share our own experiences with surgery and recovery.