Hello and thank you for your question.
Yes, your symptoms are very suggestive of acid reflux, not sinus problems.
I do not think you are under-medicated if you only take Protonix 40 mg once daily and still having such severe symptoms.
There are actually multiple options and multiple medications that can be tried. Protonix is a class of medications called Proton Pump Inhibitors (PPIs). There are several other medications within that class such as Nexium, Aciphex, Prevacid, Kapidex (newest) and Prilosec. Initially I would recommend that you increase Protonix to twice daily, if you still continue to have symptoms, you can ask your doctor to switch you to a different PPI (also to be taken twice daily).
In addition to a PPI there are several other things you can take such as Ranitidine (Zantac) 150 mg twice daily - this one is available over-the-counter, Reglan 10 mg (prescription only), and/or Carafate. All these other drugs improve acid reflux, Reglan helps with making the esophageal valve stronger so that less acid leaks out, Carafate is great for treatment of ulcers as well as general stomach healing.
So these are your options. Please discuss them with your GI doctor and see which one would be most appropriate for you. Sometimes several different combinations/dosages of drugs need to be tried before symptoms resolve. Also I am assuming that you have received treatment for H. Pylori that was found in your stomach (2 antibiotics along with a PPI). If not, that must be addressed and treated.
I hope you find this information helpful. Please feel free to follow-up with any other questions you might have.
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Best wishes and good luck,