Can the bones on the side of my nose be shaved down a little bit, without making my nose look even skinner than it is? (Photo)

The bony bumps on either side of the nasal bridge can be gently shaved or rasped down in order to smooth out the profile and 3/4 views.  Additionally, shaving these down will not narrow the nose, but make it look a little bit wider, when looking at the nose from the frontal view.  Imagine looking at the narrow "spine" of the roof of a tent and then shaving that down and you will actually be looking at a "plateau", so to speak.  My recommendation is to seek out a consultation with a double board certified facial plastic surgeon.  They will have both training in form and function of the nose.

  The dorsal hump is composed of both bone and cartilage and must be shaved down in order to remove it. Shaving down the dorsal hump will create an open roof deformity, for which osteotomies are then required. Look for a rhinoplasty specialist  who has dedicated a significant component of their practice to the discipline a rhinoplasty and performs them quite often for best results.

By definition shaving down the upper edges of the nasal bones will change the dorsal aesthetic line to a more smooth one with no outward bump. By so doing the base of the nasal bones remains the same and should not make the nose more narrow. Nasal osteotomies, however, will make the nose more narrow.