Welcome to the Healing Well Wrapped Club! I also had severe lung issues, which led me to having the surgery 3 years ago. I don't know if you've been lurking around the forum for a while and have seen my early recovery post, but just in case, here it is:
In it, you will discover that I coughed constantly and severely throughout my recovery. Like you, I worried about ruining my wrap. Don't worry...while it hurts to cough, and you're probably have struggled with a painful left rib incision (ice works best), you won't damage the wrap. It's pretty tough.
Yes, reflux symptoms are very common during the recovery stage, and I had them as well. They're worrisome, I know, since this surgery isn't taken lightly, and it's frightening to think that we went through all the trauma to our bodies without the desired outcome. Do not worry!
The esophagus is a dumb organ and it interprets all pain as reflux. Also, as my surgeon said, "pretty much anything is possible during the early stages of recovery". You can get a little reflux because your wrap is swollen and misshapen and can let a little acid through from time to time.
My lungs were extremely sick before, during, and after my surgery. It took a full two and a half months to see relief. Once they had time to heal, they seemed to get better overnight. I'm extremely happy I had the surgery. My lungs were very unhealthy ("life-threatening" were the words my primary care doc used). Since my surgery my asthma has improved 100%.
Also, remember that your wrap becomes increasingly swollen over the first two weeks or so, so don't be surprised if your swallowing becomes more difficult as a result. Once the swelling resolves, you'll be on the road to recovery.
Food, medication, and liquid can sometimes get stopped by the wrap and just sit there fermenting or irritating the lower esophagus and wrap, so be sure to take sips of liquid after eating to aid in the movement into the stomach.
I remember times when I'd burp and it would send food-tinged liquid up to my mouth, mimicing severe reflux. The difference was that it was not acidic.
Again, glad you've joined us!
It's a great place to be when recovering from a wrap surgery.
I'm sure others will be by to welcome you and share their own thought and good wishes.