Health Central has a  good foot pain section you might want to check out and do try the check a symptom box on the upper left hand of the page - it will guide you through your symptoms.

You could very well have plantar fasciitis, a fairly common but often quite painful condition that often effects the heel as well as the arch. It's caused by inflammation in the tendons and ligaments that run from the heel to the toes. Check out the link below for more information on it. There are several home remedies you can try. Given the severity of your pain it sounds like should see a doctor about this. My plantar fasciitis was resolved by custom orthotics provided by my doctor. 

http://www.healthcentral.com/chronic-pain/foot-pain.html

http://www.healthcentral.com/chronic-pain/guide-154667-75.html