Can a Deviated Septum Be Linked to Enlarged Turbinates Which then Make the Nose Look Swollen?

Enlarged (hypertrophic) turbinates are often seen in association with a septal deviation.  They make the nose appear swollen on the inside (nasal cavity) but really have no effect on the outward appearance.  However, if your turbinate enlargement is secondary to something like allergic rhinitis or seasonal allergies, then it's possible that your entire nose will swell up periodically at the same time your turbinates do (which would manifest as a stuffy nose).  A septoplasty/turbinoplasty will improve your airway and thus your breathing, but will not have an effect on the outer appearance of your nose.  

A severely deviated septum will create atrophy of the turbinate on the deviated side and a hypertrophic turbinate on the opposite side.  In other words, the deviation will compress the turbinate on the affected side and the opposite side will hypertrophy.  The deviated septum or turbinate hypertrophy have no bearing in relation to the external portion of the nose and do not affect any swelling or changes on the outside.