First off sweetie with any ongoing problem of pain it is best to see a doctor as they can give you a much better diagnoses. However from what you describe best guess would be this...
Plantar Fasciitis-In short this is an inflammation/irritation of the plantar surface (heel/bottom of foot). This pain can worsen if not taken care and then over time can lead to heel spurs. Reasons for this happening is heavy running, being on your feet on day, not stretching and warming up properly, not wearing the right shoes for arch support while doing these activities.
The symptoms are pain and stiffness in the morning that tapers until activity increase more. Pain if standing still for to long that cause you to shift from foot to foot. Pain at the beginning of a running, then less, then more when done. Not treating this some believe can lead to heel spurs which is an actual growth on the heel bone itself, its not likely you are at that point as the symptoms are different. However you need to heed this warning by taking the proper precautions.
-Switch to cardio that is easier on your feet (swimming, biking, elliptical)
You would want to minimize running, kickboxing, heavy dancing.
-Get new shoes if your are older, and really invest in a solid pair not just for working out but for your day to day activity as well.
-You may want to take a week off, sit with your feet up and really try to baby your feet. Since this is a new problem it could be a simple flare up that just needs some rest.
-Increase your flexibility, strength and balance. Alot of times we are off center, this cause more weight and pressure to reside on one side more than the other or constant alternations. Taking the time out to stretch properly and utilize balance training can do wonders for stopping these kinds of problems.