The reason why you see too much of your nostrils is the result of several issues. The cartilages that make up the lower aspect of your nose are rotated to high toward your eyes or top of your face. As a result, this pulls up on the nostrils which creates more flaring or show. Also, if your septum is long as may be the case, that is the center of your nose, this could cause your nostrils to be more visible on a side or profile view. It can be a combination of these factors as well. The procedure to correct it would be to do a rhinoplasty in order to lessen the amount of nostrils that are visible by possibly shortening your septum and/or bringing down the cartilages that form the side of the nostrils.