How come 13 old boys nipples swell up?

At 13 you begin going through puberty. When this happens your testes begin producing testosterone for the first time, some of this testosterone is naturally converted to estrogen, which causes sensitivity and growth of breast tissue. The overgrowth of breast tissue in men is known as Gynecomastia

The same thing is happening to girls when they go through puberty, but they have much more estrogen and actually end up growing breasts instead of just a little swelling/discomfort.