Can Anything Be Done to Help Nose Asymmetry After Upper Jaw Surgery?

Maxillofacial (jaw) surgery may cause displacement of the nasal septum and asymmetry of the nose.  This can be improved/corrected with a septoplasty and rhinoplasty and at the same time the metal plates/screws can be removed.  This can be done in an office-based ambulatory surgery setting under IV sedation.

Unfortunately, the picture is a bit fuzzy but I can appreciate that you have more nostril flare on one side versus the other. This flare can be do to many things.
Nasal septum (middle cartilage) may be off, the nasal muscles that are usually tightened at the base of the nostrils may have been tightened unevenly or could have relaxed, or the upper jaw may be more prominent on that side due to its position to allow your teeth to fit just to name a few. It would be unusual for the plates and screws to causes that fullness. The plates and screws are very small/thin. It is best to visit with an oral and maxillofacial surgeon or a plastic surgeon to have a complete eval as a second opinion.
Good Luck.

While the attached photo is too small to clearly assess, it's quite unlikely that merely removing the hardware would require a hospital admission, and usually swelling is much less with such a procedure.
The massive swelling that accompanies maxillofacial surgery such as you've described is primarily related to the cutting and manipulation of the bones of the midface and not merely the surgical dissection itself. As a result, airway issues and the potential for bleeding necessitate the hospital stay.
Removal of the hardware--while not trivial--is often much less traumatic since no bony manipulation is necessary.
All the best,
--DCP