Should my nose move?

The bridge is in the standard human a 50% bony (therefore solid and rigid) and 50% cartilagenous and flexible; short nasal bones may lead to a 20/80 ratio and mobility of the bridge.This ethnic feature is common in afroamericans, asians, nordic europeans and slavics.

Jesslee,

   It is not normal to be able to flatten the bridge of the nose or move it from side to side.  Only the tip moves, and even the tip shouldn't flatten down.  Do you have a septal perforation?  Do you have poor tip support?  These questions and what to do about it could be answered by a surgeon skilled in rhinoplasty.  

  The upper one third of the nose is bone which is fixed and stable.  The lower two  thirds of the nose is composed of cartilage which is flexible.  The middle third of the nose is  composed of the upper lateral cartilages, while the lower third of the nose including the nasal tip is composed of the lower lateral cartilages.  It is normal to have flexibility in the lower two thirds of the nose.  A thorough internal and external examination of the nose is required to make any determination about functional or cosmetic nasal surgery.

The cartilagenous part of a nose normally moves with finger manipulation including the profile line of the lower half of the nose if you're calling that the bridge. I suggest you have a consultation with a rhinoplasty specialist to examine you and determine what is causing your nasal obstruction. Straightening the septum and reducing the turbinates may be necessary to improve breathing.