I actually have a pinched nerve in my back from cycling that will send pain down the left arm. It doesn't affect my breathing though.
I have experienced what you are talking about in two very different situations.
1. Time trial or 5k run with inadequate warm-up. Blasting off that starting line guns blazing, and yep, nearly exactly what you described. I'd imagine lack of sleep would make this worse.
2. Drinking and riding. Downtown on a beater bike and eating a burrito or pizza plus sharing a pitcher or three with friends. If I sprint across a green light or power up a hill, same situation. Makes me wonder how burbon was ever a part of chemical cheating but it was.
So not everything is angina. It sounds like you are busy ruling it out.
The only thing I'd add would be to discontinue any non prescription meds or supplements and slowly work them back.