Hi again --
Yes, the belching and gas are pretty much the same thing, just in different areas. Gas definitely causes the lower left quadrant discomfort. Sometimes you can get rid of it easily, other times not --
Hopefully your doctors are correct that there is nothing wrong with your gall bladder. But keep your eye on those symptoms because as I said, many people here have different problems and all still ultimately point to the gall bladder. Upper right (like below/under the right rib cage area or even in center of upper abdomen) can easily be related to the "biliary tree" i.e., gall bladder, liver, pancreas, and various ducts.
Try eating fewer carbs like sugar, white flour products, and eat very little greasy or fried food. See how you feel also by stopping much in the way of dairy products.
I noticed weight loss and felt better in general after cutting out (mostly) the above items. Carrots are good, as are apples, drinking plenty of water, NOT drinking alcohol (too much sugar and the liver/gall bladder don't tolerate alcohol well), and if you like it,drink a bit of chamomile tea.
Assuming you're not allergic to whole wheat products you can easily have wheat bread, bagels, etc. and not miss the white flour products.
We need to pay attention to how we feel at different times and see if certain foods make us sick. Doctors can only do so much. It also helps to be really specific with them in describing symptoms.
Best wishes to you!