I would say definitely go see your doctor. It could be something simple like sleep apnea or even just sleep paralysis that startles you and causes a rush of adrenaline or it could be some sort of heart issue but you will have to be monitored to see what is happening. I would see your doctor and see what they think and talk about possibly having a sleep study done. Best of luck getting to the bottom of it.
As you research the issue and propose the possibilities, I would divide them into two groups. One for potential common causes, and the other for potential uncommon causes. Your description seems unusual to me. I can think of few common causes related to the heart, so if you are pursuing the idea that it is heart related, I would not rule out an uncommon cause.
As a mere arrhythmia patient, I am ill-equipped to deal with the diagnosis of something out of the ordinary (although there are other among us here whose ideas have really shined in the past). As for a potential common arrhythmia issue, the only thing that comes to mind is some type of paroxysm of tachycardia. However, terminology like "huge heart pressure" and not being able to feel extremities doesn't seem to be a fit with this.
You could also try an internist to get a systems perspective before drilling down into the heart issue path. This could save time.