Does a Septum Piercing Cause a Deviated Septum Problem?

If its the side of your nose (the most common site), then your septum won't be affected as its located in the middle of your nose. If its truly the septum then its unlikely to cause a deviated septum. This is because its the membranous septum which is pierced. This is the fleshy piece between your nostrils. A deviated septum refers to the cartilaginous (and sometimes bony) part further inside your nose. However it can be the cause of a few problems. If an infection occurs and spreads up into your nose it may cause the cartilage to soften and melt away. If the hole elongates with time, the collumela can droop.

The number of women undergoing nasal piercings has
dramatically increased in recent years.When these piercings involve the nose in the area of the nasal septum,
there’s a significant potential for complications.These might include chronic infection, chronic
perforation and distortion of the nasal septum.In some cases the nasal septum might curve with resultant distortion of
the nasal tip. All of these problems can
be extremely difficult to treat. For these reasons, patients should think twice
before piercing their nasal septum.

Nasal piercing of the ala (nostrils) should not affect the septum.
Piercing of the columella (center/base, near where the nose meets the upper lip) may cause or worsen a deviated septum. Piercing in this area may also affect the cartilage of the tip of the nose by damaging the cartilage.
As I understand, septum piercing should go through the membranous part of the septum. This area between the cartilage of the septum and the cartilage of the tip of the nose. This softer area can be moved from side-to-side.
Speak with an appropriate surgeon to perform a comprehensive evaluation before piercing the nose.

You should be more worried about creating a septal perforation ... or a permanent hole in the middle of the nose.  This would create a life long irritation in the nose with bleeding, crusting, nasal obstruction and commonly a whistling sound when you breathe through the nose.  Secondary repair of this issue has overall dismal percentage success rates in even the most experienced hands.  If you are just piercing the side of the nose or columella (area between your nostrils) then you should not have any concerns.  But you may want to think twice before setting yourself up for a lifetime of problems!
 

A nasal piercing MAY cause much more than a simple deviation.
The piercing is done near or through the (vertical) septal cartilage. If the wound now or in the future becomes infected, the surrounding cartilage can literally melt away. This results in a larger hole with collapse of the tissue and structures nearby.
Depending on the extent of such loss, the tip of the nose and middle of the nose may lose support - either one results in a BAD cosmetic result which is hard to repair and which would be MUCH more expensive than the original piercing.
Listen to your mother!