Big chest how exactly?
Fat? A “barrel rib cage” Large/defined pectoral muscles??? Wide and tall or deep?
There are various exercises for developing pectoral muscles – the push-up works the pecs, so too the bench press and then there are machines that work on the pecs as well.
There are even exercises which work as separating or increasing the distance between each rib making a bigger chest cavity.
Nipples are genetic, some people have innies, some have outties, some have large, some have small, some have ones that “sag” and some have ones that are “perky”.
although a bigger chest (working the pectoral muscles) will increase the size of the muscle underneath, thereby stretching the skin on top, causing the nipples to spread further apart and in many cases “twist” slightly (it has been noted that nipple piercings once going horizontally in people who worked out and built up their pecs have turned diagonally) the over all affect can be just a little or it can be a lot. It depends on your genetic make-up.
since you are 'skinny' it is possible that you have a body type which is prone to low body fat and may be difficult to pack on muscle mass – although you would get stronger with your workouts you may have just denser muscle not bigger muscle.
Ribcage expansion exercises may be your 'best bet' usually in the form of pull-over exercises where you pull a weight from over your head – a simple exercise is where you rest your upper back on a bench head and shoulders out in space and raise and lower a weight “over” your head. It will slowly cause the cartlige between your ribs to stretch making you have more chest cavity. This is usually part and parcel of an exercise program that works out all muscles since proportion is always key to looking good.
Not only is it for good looks, but a man who works out nothing but his top (chest/arms shoulders/back) doesn't have the real support (legs/buttocks/lower back) to support the strength he can apply at the top leading in many cases to lower back and leg injuries.