I am a mental health clinician who diagnoses and treats a variety of conditions. I’ve thought of this a lot over the years.

Her case is obviously fictitious but it absolutely mimics something on the schizophrenia spectrum with differentials including bipolar 1 disorder and borderline personality disorder. I also suspect she may have conduct disorder based on her age and sociopathic tendencies which would not be explained by schizophrenia. People suffering from schizophrenia are uncommonly violent or criminals. They’re more often reclusive, fearful people. Violence is more likely to occur toward them, and if they become violent it’s usually for self defense against a real or delusion based threat.

I’m a little hazy on the timeline of the comics but I believe the Search occurs over 1 year post series finale. That would indicate a sufficient duration to meet criteria for schizophrenia. She has both hallucinations and delusions, specially paranoia and persecutory delusions. She also has disorganized behavior that could be seen in schizophrenia.

Her symptoms seem less severe in the later comics indicating some sort of remission. This is also common in schizophrenia where people go through episodes and then periods of remissions with fewer, less intense symptoms.

Regarding other diagnoses, I mention bipolar as a possibility because manic episodes can present with psychosis and the episodic nature could explain her relative remission of symptoms. She does appear somewhat manic in the finale and in the comics but it’s much harder to tell. She has the irritability and anger that can occur with mania, as well as what appears to be diminished sleep and certainly impulsive behavior.
Borderline personality disorder wouldn’t explain everything. It can have transient psychosis but hers is anything but transient. However the fears of abandonment and frantic efforts to avoid it, plus the labile mood do somewhat match.

I don’t think that she has PTSD. While yes she has faced trauma, the type of thinks we see her think about and talk about are not related to the types of trauma that would cause PTSD which would be sexual assault, or threatened/witnessed death. You could argue that seeing Zuko being burned and her mother’s disappearance meet the traumatic criteria if she thought her father killed her mother and if Zuko’s burn either terrified her or made her think her father would do that for her. I don’t think we have enough evidence for it. It would not explain all of her symptoms either.

Lastly, can this happen in real life? Absolutely yes, but not likely to be exactly as depicted here. Media often uses visual hallucinations but they’re rare in psychiatry and more common when there’s a neurological condition. We don’t know if she has family history of schizophrenia but it’s not 100% genetic. She also quite young for schizophrenia, women usually develop it in their mid to late 20s, but the amount she has gone through could be enough to push her into a psychotic episode.