There are a few disorders aside from celiac disease that seem to improve drastically on a gluten-free diet. One of those disorders is schizophrenia.

A new article just published in the World Journal of Biological Psychiatry shows once again that there is a link between reaction to gliadin and schizophrenia. The team from University of Maryland Medical School studied 950 schizophrenics and 1000 controls. They found that the levels of antibodies were about 50% higher in schizophrenics. The implication is that a gluten-free diet may prevent the development of schizophrenia.
http://www.ncbi.nlm.nih.gov/pubmed/23282016

An earlier study done in China contained 473 schizophrenics and 478 controls and got similar results. In the schizophrenic population 27.6% of females had the reaction to gluten vs 13.9% if the controls. For males the numbers were 26.4 of schizophrenics and 19.8 of controls.

You can read the Chinese study results here
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3330001/

And back in 2011 they did another study in the US which compared the level of reactivity in the blood. Again, the numbers are much higher in the schizophrenic population than in the control group and again there were 1400 schizophrenics and 900 controls. Here over 10 times as many celiacs as controls who reacted to the protein.
www.ncbi.nlm.nih.gov/pmc/articles/PMC3004201/

I would call this a pattern. But there are even more studies that indicate a strong causal link.

Which leads to the really big question “Can a gluten-free diet reverse schizophrenia?”

The answer seems to be “maybe”

The original work that started this line of inquiry back in the 1980s was done in a psychiatric hospital where the schizophrenic population was put on a gluten-free diet. Some of the people recovered completely. Most did not. Here are a few of the older papers on this topic. Note that there are some tales of recovery.
http://www.ncbi.nlm.nih.gov/pubmed/16423158
http://www.ncbi.nlm.nih.gov/pubmed/3524724
This woman also recovered
http://www.ncbi.nlm.nih.gov/pubmed/9408073

The evidence so far is thin at best but if it was me, I would go on the diet if I had any concerns about schizophrenia. Although there is nothing conclusive, the evidence seems sufficient to warrant taking on the risks involved with changing my bread and cookies.

Again I am not a medical doctor, and you should discuss this with your psychiatrist, but at least now you have the data you need to have that conversation.