Why could you have purple spots on your chest with heart pain?

Purple spots? . It's hard to be certain by your description, but your words, "purple spots" make me concerned about a condition called "purpura". These are due to bleeding under the skin and suggest insufficient number of platelets. This is a serious condition. You need to be seen asap. This is a pretty good reason to go to the er!
Doctors can evaluate. Rashes and spots are difficult to describe in words. Purple can be bruising, which is blood leaked out of skin capillaries (tiny blood vessels). Some abnormal clusters of blood vessels in the skin, or some skin tumors, can also look purple. Heart pain is, of course, a serious problem that should be closely followed by a doctor. That doctor, plus a dermatologist, can evaluate the purple spots.