Very Sensitive Nipples 3 Years After Breast Augmentation?

It is unlikely that the recent sensitivity changes you've seen are a result of your surgery.  Temparary changes after a breast augmentation are relatively common.  Some patients become more sensitive, some patients claim to be less sensitive.  Permanent sensory changes are rare.  Over the years I have seen a handful of patients who have developed similiar symptoms to yours.  For some unknown reason they developed what appeared to be a rash of one or both areolae years after surgery.  Their symptoms cleared up with a topical steroid.  Your best bet is to be evaluated by an experienced board certified plastic surgeon in your area. 

Nipple sensation can be affected by breast augmentation but this is usually in the early postoperative period.  Sensation can be decreased (more common) or increased.

The symptoms you describe with dryness, pain, and peeling do not seem to be related to the breast augmentation.  This may be due to a skin disease or sensitivity to fabrics, chemicals, or environmental exposure.

This is something that you may want to have your PCP or a dermatologist look at to determine if something can be done to help improve your symptoms.