Puffy nipples - An isolated issue or do I have tuberous breasts? (photo)

It looks like what is called a herniated nipple/areolar complex. Without an in person exam it is difficult to tell, but it looks like there may be some constriction of the lower pole.
This can be corrected with surgery which releases the constriction of breast tissue that pushes the areola out. Some manipulation and repositioning of the breast tissue may be done, and the areola can be reduced in size. Once the constriction is released, an implant, if desired may give a rounder contour. An implant alone or a procedure removing just some areolar tissue doesn't work unless the puffiness is very small and without constriction.

It appears that you have puffy areolas/nipples, no underlying tuberous breasts. This can be corrected with a simple procedure in local anesthesia. You should look for a plastic surgeon familiar with this correction. Good luck.