Have you been tested for helicobacter pylori? (called 'Hpylori' in the medical world). This is the bacteria that lives in the stomach and which causes peptic ulcers. These ulcers, if left untreated long term, can cause cancer so it's important to get the blood test firstly, just to see what's going on.
It is a simple blood test which can be cured with a regimen of antibiotics. If you don't have Hpylori, long term medication can help too, like Ranitidine & Nexium.
As to natural treatments, you can start by keeping a diary and see what triggers your acidity levels - you said it was stress - some say it's certain foods, drinks like coffee, eating late at night, etc.
Cooked, cooled white rice is good for acid indigestion, because it helps soak up the acid your body is producing. Keep it in the fridge after cooking it first. Have a few tablespoons at night before retiring, as when you lie down, the acid regurgitates up from your stomach into your oesophagus. This is usually from a 'loose' oesophageal sphincter. (You don't usually get as much acid indigestion when you're walking around upright, as gravity helps keep the acidity down).
If the problem persists, you need to get an endoscopy to check out what is happening as acids can cause oesophagel cancers. The acid eats away at the tissues and destroys them, changing and damaging the cells.