Could the new freckle under my right nipple, on the areola, be a sign of cancer?

Yes. While rare, it is possible to develop skin cancer on the areola. Worrisome signs include a mole that is irregular, raised, ulcerated, or bleeding. When in doubt, it is best to seek out the opinion of a doctor. A simple biopsy can be performed in the office to determine if it is a cancer.
Highly unlikely. But.. All changes to a breast exam should be followed up on.. With repeat exams, more diagnostic studies (mammograms or ultrasounds, or mris), or a skin biopsy. Paget's disease of the nipple has to be ruled out in some cases.