Not every man is going to be built the same way, just like not every woman is. And very few men OR women are going to look exactly like what the images we see in movies and TV and magazines make us think we're "supposed to." That's just normal human variation. Take a look around you, and you will see that some guys have broad shoulders, some guys have narrow shoulders, some guys have barrel chests, some guys just don't.
What you're really "supposed to" look like is YOU. Look at your dad and his brothers (if any), and at their dad, and your mom's dad and your mom's brothers (if she has any). That's going to give you a much more realistic idea about what your body is really "supposed to" look like, in terms of what your genetics will tell it to look like.
That said, yes, to a certain extent, you can bulk up your shoulders and arms and chest through exercise, such as weight lifting. It can't make a guy who's built like a beanpole into Arnold Schwarzenneger, though. Nothing can. Beanpoles are gonna be beanpoles -- they might be slightly thicker or more muscly versions, but they're still going to be beanpoles, no matter how much they exercise. So exercise and enjoy it, but don't expect it to completely rearrange your anatomy!
As for puffiness around your nipples, that's completely normal for men and women alike. It can change somewhat as your amount of body fat changes, because the breasts in both men and women are places where fat is very easily and naturally stored (women's breasts are primarily made up of fat, in fact). But it's very normal. Unless you're having pain, it's nothing to see a doctor about, and nothing that any doctor can treat.
Start a Revolution -- Stop Hating Your Body!