Are my breast just never going to develop? At 20 they are still puffy triangle nubs I got at 13. Would surgery even fix this?

It appears you have tubular breasts. This is caused by a constriction of tissue around the nipple/sareolae, giving you an undefined breast fold and areola puffiness. It isn’t generally considered a health issue, if you dislike the appearance surgery can be performed to release the constricted tissue. This would give you a rounder breast shape. 

Thank you for sharing your photos. You do appear to have something we call “tuberous breasts”. To correct this, you will need more than a basic breast augmentation procedure. Tuberous breast correction is a very meticulous and specialized procedure, which should only be performed by a board-certified plastic surgeon with extensive experience in this area. My technique uses a breast implant in conjunction with a periareolar incision for reconstructive tubular breast surgery, as provides the highest degree of control and accuracy when placing the implant. This surgical technique results in a natural, symmetrical, and full breast appearance. In order to restore a more ideal and rounded breast shape, you may also recommend a breast lift along with the augmentation. Each patient with tuberous breasts is unique, and so is their surgery. I would need to consult with you in person to determine the best tuberous breast correction surgery approach.

Hello and Great Question. I appreciate the time you are spending researching this procedure. My name is Dr. Matthew J. Nykiel. I am a Board Certified Plastic Surgeon, a Fellowship Trained Cosmetic Surgeon, and a Cosmetic Breast Augmentation Specialist. 
Based off your photos your breast are tuberous, its very common and can be improved with release of the breast tissue and breast implants , I would highly suggest you do an in person consultation with a board certified plastic surgeon who specializes in this procedure and who can go more in depth on what is needed as well as do a full evaluation.
I hope that helps! Best of Luck! 
Matthew J. Nykiel, MD #CoreAesthetic Breast Augmentation Specialist Board Certified Plastic Surgeon

Any breasts that have an element of constriction or tuberous characteristics can be released and filled with either an implant or fat. Find a board certified PS who has performed similar surgeries, or even one that specializes in tubular breast modification.

Based on your photos it appears you have some characteristics of tuberous breasts.  Surgically releasing the constricted tissues and adding an implant should help improve the overall appearance.  I encourage you to meet with a board certified plastic surgeon in your area to learn more about these procedures.