I have no medical training. So please following with a grain of salt and do your own research. However, I'm dealing with similar issues and wanted to share what I've found on my own journey over the past few years.

It's possible your acid reflux is not only caused by anxiety, but that it signifies changes in the composition of your gastrointestinal bacteria which could itself be contributing to anxiety and acid reflux. There's been more and more research recently linking differences in gut bacteria between different people and differences in their health and behavior. At first I only saw this theory being discussed in 'alternative' venues, but recently I've been seeing more and more come into the mainstream -- a book called Missing Microbes was published last year by someone who worked at the National Institutes of Health, proposing that overuse of antibiotics (among other factors) is altering many people's gut microbiomes to the point where immunity starts breaking down and pathogenic microbes start inhabiting their digestive tracts. Besides causing digestive symptoms, toxic substances produced by these microbes can affect the brain.

Again, take it with a grain of salt, but according to one book I read (Gut and Psychology Syndrome by Natasha Campbell-Mcbride), the Omeprazole may be making things worse in the long run. The author theorizes that acid reflux is actually a problem of low stomach acid, rather than too much. Not producing enough stomach acid may allow microbes to grow around the LES (Lower-esophageal sphincter) that normally wouldn't be there, producing substances that paralyze the LES and prevent it from closing fully (in the absence of food coming down the esophagus).

The author also proposes that many different factors can affect the composition of gut bacteria - a diet too high in grains or sugar, severe stress, additives and preservatives in food, pollutants from the environment, etc. I can't say that I recommend the strict diet that she prescribes (had to be hospitalized for ketoacidosis after trying it myself -- still don't know whether it was due to the diet itself or food poisoning), but I do have to say that by incorporating the basic tenets of the diet I've been able to make small improvements in my reflux. There are also less restrictive variants (Specific Carbohydrate Diet, for example), but I just didn't have the motivation or energy to try another diet after that disaster.

It seems like the common tools used by doctors (proton-pump inhibitors and GERD diet) to deal with acid reflux are intended solely reduce symptoms, in the absence of any solid understanding of what causes them in a large number of people. My endoscopy came up blank except for a change in the Z-line of the esophagus and my gastric emptying test came out normal. Doctors haven't been helpful in identifying what's causing my reflux, fatigue, etc.

I've been around a lot of other people with mental illness and I can't shake the observation that so many of them have digestive issues, eat a diet high in wheat products and high fructose corn syrup, etc. I was just talking with a girl on the bus yesterday who has the same anxiety-GERD thing going on.

In the end I'm stumbling through the dark just like you are. But it never made sense to me that my issues are purely genetic, like doctors seem to assume when they don't really know what's going on. The research I've done and the connections I've made make me believe that my anxiety, depression, fatigue, and digestive issues are all linked to a surprisingly great degree, that they reinforce each other, and that they are part of a greater systemic issue. Maybe I don't have the specifics down yet, but I know I'm on to something.

If you're interested, maybe we could keep in touch and trade observations.