The occurrence of “dizziness” associated with “tightness in left chest/armpit” but not experienced in the gym may have something to do with the intensity of exertion in the two circumstances. But finding the reason for the discrepancy is not the important issue. The fact that you experience these symptoms under any circumstance is the issue and, as such symptoms are consistent with the diagnosis of coronary artery disease (CAD), they must definitely not be ignored.
I strongly encourage you to consult with your physician who, in all likelihood, will arrange for you to have an exercise test conducted in a hospital or clinic (that is, in a controlled environment) with monitoring of your cardiac function with varying levels of exertion. There exist a number of protocols for such testing but a common one is called a Stress Echocardiogram.
Do not delay arranging for testing and, in the meantime, avoid strenuous exercise or exercise of any degree that gives rise to dizziness and/or chest tightness.
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