@awnlee jawking
My understanding is that 'puffy nipples' is a medical condition of the underlying breast tissue rather than anything affecting the nipples themselves, and 80% of cases are men. And, if I had ever read any kiddie porn, I might have noticed it used as a synonym for 'breast buds' in newly pubescent females.
Huh...? Could be, maybe, but then, does such a condition has a medical name?
Just so it's clear, my understanding of "puffies" describes neither the breasts nor indeed the very nipples, but pronounced areolas that protrude sharply forward from the dome of the breast to then round up their own mini dome on with the nipple then sit projecting further when erect.
Such areolas may eiter stay elevated all the time, or only be engrossing sometimes (with arousal? may or not be limited to that), in the whole creating, as if three-stage telescoping design -- as opposed to just a dome with a point, but with a smooth sharp cone overall as the transitive form where the puffiness (as in, is that puffies or not) wouldn't be defined.
The baby milk bottle rubber cap is rather accurately modeled after such form of the areola, so it's associated with breast feeding to at least the same degree as with pubescent breast buds, with, imho are more likely and often of the overall conical rather than three-stepped designs. However, it's a staple for barely-post-puberty teen girl breasts, especially when combined with smallish perfectly firm breasts shaped from cones to half-spheres with zero sag, where in a silhouette or section drawing the upper and lower curves would be nearly ideally mirrored on the nipple. I call such with puffies, the cone type particularly, "forever fifteen" breasts, and have seen such on all ages including woman in her fifties in real life.
"Puffies" are a somewhat rare-ish sub-genre in soft porn erotic images and some models are known to use vacuum pump (apparently, purpose built?) to simulate/stimulate/exaggerate the effect.
I have tried to coax AI image generator to draw them, to almost no avail, although it's not like it haven't seen such. It sometimes decides for them randomly, mostly, if the promt emphasizes sexual activity very heavily. Unfortunately, at that point there's host other deformities that become very likely, including, but not limited to, overly enlarged breasts that I, not necessarily dislike, but surely didn't target. More reliable language, or more options to describe such succinctly would be very helpful with that, if not otherwise.
In one writing attempt I have tried to describe such using the tiny Turkish coffee cups for reference, but doubt that was very clear or efficient, even less erotically effective.