Psychotic Disorder NOS can be a temporary diagnosis, but many times the symptoms just don't fit into other serious mental illness categories, and will be tagged with the NOS specifier. In reality, true SMI patients have a multitude of symptoms that are not textbook. They are very diverse and personal, dependent upon many factors, including past and current history, values, beliefs, etc.
I love reading this type of story and of course, always critique the mentally ill characters as well. However, as long as it is not too far fetched, it is believable, and many lay people really aren't aware of how the true symptoms should be portrayed. A beautiful Mind, although may have taken some liberties, according to text book, but could be believable, and was, based on its popularity.
I do work in an inpatient hospital for the seriously mentally ill, and it is not uncommon to see patients with fixed delusions and auditory, visual, olfactory, and tactile hallucinations. Most of these patients clear with appropriate medications, but not all. And many admit and discharge with the diagnosis of Psychotic DO, NOS. So....I do think this is a believable diagnosis given the symptoms your character exhibits.
Hope this helps. Gina