A buildup up acid in the esophagus can cause those symptoms, they did for me. I have a lot of experience with angina, but this felt different in that exercise didn't make it worse. Like you, it would just come and go, at random, even if I was just sitting in a chair. If acid leaks up into your esophagus, it causes inflammation, which can be painful, and cause you to feel light headed because your vagus nerve can be squashed. Being stressful does affect acid levels so it could be related. You don't say if you feel pain, but like heart attacks, I suppose everyone can be different. It doesn't have to be related to gas either, but if left, it will usually get worse. The sphincter which prevents backflow of acid will get inflamed and damaged. Why not get some strong over the counter anti-acid and try that. I found Gaviscon worked fine, but it took a couple of days to get rid of it. As a precaution, I have been put on proton pump meds for life (omeprazole).
I used to have a similar feelings. Turned out I was hyperventilating (stress related). I learned to simply take a big breath and hold it. That usually did the trick. Breathing into a paper bag should also work.
I also found out that chewing maalox would really immediately help with burping and gas (well, you will burp even more for a few minutes till the gas build up is gone).
Try and get out and exercise. It really helps with the stress.