Did I have a mild heart attack if I have chest pain not due to injury pain in upper back, left side of neck down to elbow w/strong fam hist of heart?

Can't say. Wouldn't know without an ekg. But with those symptoms and your family history i hope you submitted this question from the er waiting for an ekg!?
Probably. You should see your doctor asap or go to an emergency room, call 911 if needed for transportation. There may be time to intervene and prevent additional damage to the heart.