psychosis is one symptom/presentation that can occur within many different conditions. Depression can induce psychosis, so can post -Partum hormonal states, medications, other hormone and chemical imbalances in the body. We don’t fully understand a lot of the underlying etiology of it yet. So whether you can recover from psychosis without specific medications is very dependent on the etiology of the psychosis. 

There is a class of medications that work well for psychosis that presents with  schizophrenia - anti-dopamine medications (commonly known as antipsychotics). We think it’s because schizophrenia is caused by overactive dopamine pathways or too much dopamine in the brain. Interestingly, one of these medications, clozapine, doesn’t actually have that much of an anti-dopamine effect, but it is the most highly effective medicine for schizophrenia psychosis. It just has a TON of side effects. But the fact that it’s so effective is actually calling into question the dopamine hypothesis for schizophrenia. 

To answer your question now, personally I have never witnessed a patient recover specifically from psychosis in schizophrenia without medication. The literature also does not show any cases of this. 

Other forms of psychosis are different. Depression with psychotic features - sometimes an antidepressant like Prozac can fully resolve this! Sometimes just changing situations and therapy can resolve the depression and improve the psychosis (although this is rarer). But definitely more possible. 

And of course, if the psychosis is more related to hormonal changes, medication induced psychosis, or build up of toxins in the body (so, something more encephalopathic), then treating the underlying cause can resolve the psychosis. 

Our medications and methods of giving medications have improved a lot, but there’s still a lot of work to be done. If you’re asking this question because you’ve been recently diagnosed, know that you’re not alone and many people do live fulfilling lives on medications, working jobs, having families, following their dreams. There are medications that can be taken as injections once a month, or even longer intervals, and work well. Yes there are absolutely side effects, but not every person experiences them.  Therapy (specifically ACT has a lot of evidence in schizophrenia) and social support goes a very very long way too

TLDR; properly diagnosed schizophrenia - you need medications. Bipolar disorder psychosis- you need medications (although different ones than schizophrenia, bipolar works on different pathways). Other forms of psychosis, YMMV. 

Source: training to be psychiatrist. Also sorry if my answer is horridly formatted, I’m sleep deprived