When I first started working out my deltoid area - with planks and push-ups, I experienced a little of this. I've learned it has to do with muscle imbalances. My right side is stronger than my left, so when I do exercises that even it out, my left side feels it.
When I started doing Ashtanga yoga, I had a little of this with the muscles around the lungs . . . due to deep breathing.
There was an old ER episode where a new intern was about to inject a healthy-looking patient in the chest with something that is supposed to jump-start the heart. The doctor said to the intern, 'what are you doing.' The intern said, 'I'm injecting him with (whatever it was called) since he's haviing a heart attack.' The doctor asked the patient, 'did you do any strength training or heavy lifting yesterday?" which he answered yes he had. The doctor then explained to the intern to always ask patients if they've worked out the deltoid muscles because they have similar symptoms to a heart attack.
I wonder if it could be a shoulder/deltoid muscle stress thing. Just a thought.
*I'm not a doctor, but I watch them on tv