Can Rhinoplasty Enlarge or Widen a Tiny Nostril?

If you have two different shapes to your nostrils that can signify alot of things including a deviation of your septum. I agree that the only way to make something bigger is to add something there. Typically a cartilage graft is needed and likely a composite graft (composed of two parts, skin + cartilage) will be needed if it is in fact a stenotic nostril. Post procedure you may need stenting to support your nose during the recovery period.

Rhinoplasty alone does not usually change the nostril size or width much unless one does an alar base resection or nostril base excision. These are separate entities that are an intrical part of a rhinoplasty if you want to create facial and nasal balance especially in males and/or Ethnic patients.

There are a variety of techniques for changing the shape of the nostrils, including those for enlarging asymmetric ones.

Rhinoplasty technique can in some instances be quite successful in opening a small nostril. In some cases this can be a result of congenital weakness of the underlying nostril framework (cartilage). If so, this can sometimes be reinforced with additional cartilage (termed grafting) to help open the nostril further.

In other cases, this might involve what is termed a composite graft, which is a specialized graft containing cartilage and skin together. Keep in mind there are definite limitations to how much larger the nostril can be made. You also need to be realistic and accept the fact that most people's nostrils are asymmetric to some degree.  

As you can imagine, it is easier to reduce the size of a nostril than widen it. That being said, nostril enlargement can be performed but the process by which it happens can depend on the cause of the nostril reduction in size.
If it is related to scar from trauma or surgery, then scar release procedures and tissue grafting will often help. Sometimes a small nostril is really just an unsupported nostril that needs cartilage grafting to support it staying open. If tissue is missing and this is the reason that the nostril is small, then adding tissue back in the form of a composite graft or forehead flap may be necessary.
In the end your surgeon needs to take a good look at the anatomy of your nose to determine what is going on. This will allow them to better decide what procedure will help.