Beyond the problem of assessing the rates of mental illness in Egyptian times, the more pressing issue is that modern psychiatric diagnoses--schizophrenia, PTSD, depression--did not exist then, and it would be a serious error to try to remove labels from time and place.

Yes, the hallmark symptoms associated with schizophrenia were likely present then: delusions, hallucinations, flat affect, etc. But schizophrenia, as a label used to define people, was a consensus of psychiatric committees and of practitioners in the 20th century. As thoughts about the origin/neuropathology of schizophrenia changed over the years, so did the thoughts about what type of person was susceptible. Who was the model patient?

(Jonathan Metzl wrote a really good book addressing this phenomenon called The Protest Psychosis. Here's a link to an interview with the author for some additional reading: https://www.psychologytoday.com/blog/side-effects/201005/how-schizophrenia-became-black-disease-interview-jonathan-metzl)

The real problem here is of labels. Specifically, they are never a fixed thing. Labels are not just levied down onto people from psychiatric committees, but also people act upon their descriptions. This looping effect changes medicine's definitional categories, which then recasts who is sick and who is healthy. Rinse wash repeat over decades. This is why schizophrenia is a moving target of modernity and cannot be wholly understood in Egyptian times.

For this point, Ian Hacking isn't recommended reading--he is essential reading. I'd start off with chapter four (pg. 100) in The Social Construction of What?: https://larvalsubjects.files.wordpress.com/2011/01/hacking-the-social-construction-of-what2.pdf

This is pretty dense stuff and it took me well over a year of grad school to scratch the surface. Reading Hacking is difficult.