Hey man,
I have it exactly the same as you... I got "buds when I was about 11 or 12, and they felt kind of tender under my nipples when I pressed them, I never thought much of it since it didnt hurt unless they were touched. But then I started to get embarrassed of them around 13 or 14. thats about when the tenderness stopped in my nipples.
Now I'm almost 16 and I think they have gone down a little tiny bit (if any), but if somethings happening, its going waaay to slow, they say 90% of these cases resolve during/after puberty, but Im not buying that large of a percentage.
My advice to you is just not to gain any weight, get in as best of shape you can get in, reduce your body fat, run as much as you can, play sports, and do a little bit of weight training at 13, then slowly increase the weight lifting when you get older. The nipples will still be puffy if you build up chest muscle, but I think it will make it look a little bit better. and btw I was 5'5" 120 at age 13 too... good times!
Hopefully our nipples go back to normal.. good luck man!