Do I have puffy nipples or tubular breasts? Could this be corrected without implants? Price? (Photo)

If your breast look like the photos, then this does look like tuberous deformity. If you don't want bigger breasts then this can be corrected by circum-areolar (around the areolae) skin reduction.
Regards, Dr Steve Merten, Sydney, Australia

Thank you for the question. The photos you have posted do  demonstrate features of tuberous breasts.
 Some of the characteristics seen with tuberous breasts include a very narrow base, short distance from areola to inframammary fold, tight (constricted) lower pole of the breasts, relatively wide space between the breasts, "puffy" and areola and some degree of ptosis (drooping).  
Generally,  correction of tuberous breast anomalies generally involves breast augmentation with areola reduction / mastopexy procedure. The distance from the inframammary fold is increased (to create a more rounded out appearance). Proper implant positioning improves the distance (cleavage) between the breasts. The areola reduction helps to treat the pointed and "puffy" appearance of the areola.
 When you are ready, please make sure you consult with well experienced board-certified plastic surgeons who have significant  demonstrable experience with this type of surgery.
I hope this helps.

Thank you of the question.  Puffy areolas are fairly common and can be caused by a number of factors.  If you do not want an implant, correction of puffy areolas may be addressed by an areolaplasty.  Doing so will change the tissue forces around the areola and can help push/pull on the areola tissue to flatten its appearance.Have a great day.Dr. Remus Repta

Thanks for your question. This is a bit of a tricky case. I do think an implant augmentation would help to blend in the appearance of the nipple-areola on both sides. I don't think I would recommend much else given your young age and the chance for problems w/ nipple sensation and breast feeding. I hope that helps you a little.