I can sympathize, as a past GERD sufferer. For those who are not familiar with this condition, let’s define it. Gastroesophageal reflux disease is a condition where the valve at the top of the stomach, through which our esophagus leads, weakens and in certain situations acid can back up into the esophagus leading to the burning feeling often called heartburn. The causes can be too much stomach acid, or chronic acidity even when no meals are being digested, to problems with the valve itself. Certainly, if the valve is weak turning the body upside down will make the stomach’s acid more likely to pour into the esophagus, and combining an inversion with abdominal pressure will matters even worse. It sounds like this is happening in your case: the combination of the inversion, along with the pressure in the abdomen from Snail (Plough) Pose is forcing stomach acid past the valve into the esophagus.
If that is the cause, the solutions range from the obvious - don’t do Snail! - to the sublime: how to turn off or at least turn down the acid levels in your stomach. Certainly, I would suggest for now that you remove Snail pose from your practice. Instead, do Caterpillar and Legs-up-the-wall poses to touch the same areas. Then, get to work on removing the underlying cause of your excess acidity or weakened value.
Traditionally, doctors will prescribe a drug called a PPI (proton pump inhibitor) to reduce chronic stomach acidity. I was on these for several years. They worked, but there are long term side effects for some people and I searched for other ways to get by. In my case, chasing my diet was all it took. I adopted a much more Ayurvedic diet and avoid hot, spicy foods. Avoid carbonated beverages, Avoid over-eating until you feel stuffed. Avoid caffeine too. In my case, this was sufficient to get off the PPI and I no longer have GERD.
However, there are other yogic techniques that have proven helpful. Yoga International reported on the effectiveness of pranayama in reducing GERD. This was a study reported in The US National Library of Medicine
in 2013. Their recommended procedure was the pranayamas called Agnisar kriya and Kapalbhati: “Kapalbhati and Agnisar kriya may be particularly useful in addressing GERD as they can increase diaphragmatic tone, thus decreasing reflux from the stomach to esophagus. ” In short they found “Practicing yoga in conjunction with medications can be helpful in controlling and/or alleviation of symptoms related to digestive diseases.”
GERD sufferers who do yoga as well may get a lot out of reading the full article.
I hope this helps!