What is wrong with my nipples? I'm not sure if I have puffy nipples or something else but I hate the way they look. (photo)

Thanks for your inquiry.  I do not know of a procedure that would eliminate your concern.  With time and pregnancy I have noticed that the general puffiness of the areola does often reduce, but I have also seen in a few it has gone up.  Hope that helps.  

Don't be discouraged. Seek out a personal consultation with a board certified plastic surgeon. You may have some variation of inverted (pulled inwards)  nipples. There are procedures that can be performed under local anesthesia to correct this. I attached a link to read some information about this corrective procedure. Hope this helps.