The surgical procedure is called Nissen Fundopliction. It is a laproscopic surgery, so it's much easier to recover from than an open surgery. The surgeon takes the top of the stomach and wraps it around the esophagus--creating a valve (the surgeon actually said it's more of a one-way flap--to keep the food and acid in the stomach where it belongs.
If you go to the Heartburn/GERD forum at Healing Well, you can look up my old posts, which describe my recovery. Be careful searching online. There are a lot of people who had bad surgeons and poor results. Those people scared me into waiting four years for the surgery. The recovery is not at all as bad as I was expecting, but it is challenging, since it takes time for the new valve to reduce swelling/inflammation, etc.
I can just say that the surgery recovery wasn't as bad as all the GERD/asthma episodes I had before the surgery.
Good luck in making your decision. If you consider surgery, be sure to post at the Heartburn/GERD forum. There are many supportive and knowledgable people there, who will be glad to talk to you about it. It's a very active forum. Good luck getting insurance!
Take care and I hope your asthma is doing better.