Yes, of course you are. That was clear when you were born. When are you going to die is a better question.
If you are intelligent enough to operate a computer and write a note on ARRSE you are intelligent enough to call your Doctor. Do it now!
Doctors may take forever making appointments for a sore toe but if you call about chest pains, esp exercise related chest pains they will see you soon or send you to hospital.
He/they will brobably do an ECG which doesn't hurt except for when they rip out chest hair pulling off the taped on thingies. They may also do a blood test to check for heart damage.
I am septic type but have some medical experience w. NHS when I had chest pains on a transatlantic flight and was taken by ambulance to hospital near Heathrow. Medical care/nursing care was excellent. Only criticism was 1) urinal far too small for someone getting large quantities of IV fluids 2) they fed me something called "Shepards Pie" that clearly had been made from a very old,tough, gamey shepard.
It turned out to be gallbladder, not heart and I had surgery back in the US which is another story but turned out OK.
Just remember if I read on ARRSE that you have dropped dead I won't be writing "RIP". I will be writing "Why didn't the stupid fecker see a doctor"
I had similar symptoms, although never when i was running. I went to the doc and it turned out to be a problem with a muscle in my back/shoulder. After a visit to the physio it was soon sorted. Alternatively do a search and look for some streches that may help.
My old O.C had a problem similar to this and found that when he went for a run he had to put and carry his wallet in the other hip pocket because being an officer and a tight gett it was a two man lift.