That sounds like anxiety to me. I used to get that in my early 20s with those exact symptoms. That was before I learn to recognize my anxiety. Breathing tools were the best solution, at different times I've needed anti-anxiety medication.

Chest tightness and panicked breathing, followed by heart palpitations with no other primary symptoms (fever, cough, etc).

This is a very stressful time, especially for high-information consumers. I wouldn't be surprised if there are thousands of people right now mistaking anxiety for COVID symptoms. Over analyzing your health can lead to some crazy self-driven outcomes too.