Can you change the shape of your nose in any way with your fingers?

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Trauma can lead to a deviated septum.  This trauma can come in the form of a constant pressure.  The cartilages of the nose can warp.  However, it is more likely that your growth spurt during puberty led to the septal deviation. 

Probably not.  I have not seen an studies that show that constant pressure on the top of your nose can influence how it grew. Trauma to the growth centers of the bone and nasal septum in your younger years certainly can change the shape and deviate the septum.