My nose goes crooked when I smile due to severely deviated septum. Will a septoplasty fix this? (Photo)

It is possible that your smile might be a bit straighter after a septoplasty.  It is absolutely possible to make a functional and cosmetic change with a septoplasty alone in some cases.  This is why anyone who operates on the nose should be a master of septal work, IMHO.  Thanks.

Nasal deviations are very commonly due to septal deviations although asymmetries in the lower or upper cartilages or bones can sometimes be the cause.  A septoplasty can sometimes correct a deviation, but if the septum is deviated in the remaining L strut after a septoplasty, then grafting in this area will be necessary.  I would recommend to plan on a complete rhinoplasty and not just a septoplasty to correct a deviation. 

A crooked nose as you describe
can largely be due to a deviation of the septum, but correcting the breathing
component may not have a full impact on straightening the nose. Many times
the upper portion of the septum (the dorsum) needs to be addressed and
straightened, which is what is done in a rhinoplasty. Furthermore, once
the septal cartilage has been altered, it is possible that the dynamics of the
tip support will result in unaesthetic changes to the tip that should be
addressed as well but that is your decision.

Septal deviation is only part of the story. You appear to have a very active depressor muscle that pulls your tip down and out when you smile. Removal of this muscle and fixation of your tip cartilages with respect to the septum (once it is straightened) is the best option to stabilize your nose. In other words, your need a full septorhinoplasty to address your septum / tip.Grigoriy Mashkevich, MDNew York Facial Plastic Surgeon

A septorhinoplasty will straighten your nose and improve your breathing if done by an experienced rhinoplasty surgeon. 

The nasal septum is the center supporting structure for the nose. When it is considered "deviated" we are referring to the central portion that controls the airway. When the internal part of the septum is crooked, the outside is often crooked as well. This outer area is what makes the nose look crooked externally.What's more interesting is that typically the nose tilts externally to the opposite side of the internally deviated septum and nasal blockage. Fixing a "deviated septum" from a functional and insurance point of view will help breathing but not external tilting of the nose. That requires more complex surgery and a rhinoplasty to correct. You should see a septorhinoplasty specialist for an evaluation and qualfifed medical opinion.