Unfortunately all three classes of FAA medical certificates do list psychosis as a DQ for a issuance. For third class, 67.307, it states:
Mental standards for a third-class airman medical certificate are:
(a) No established medical history or clinical diagnosis of any of the following:
(2) A psychosis. As used in this section, “psychosis” refers to a mental disorder in which—
(i) The individual has manifested delusions, hallucinations, grossly bizarre or disorganized behavior, or other commonly accepted symptoms of this condition; or
(ii) The individual may reasonably be expected to manifest delusions, hallucinations, grossly bizarre or disorganized behavior, or other commonly accepted symptoms of this condition.
It might be possible to obtain a special issuance medical, per 67.401, but it will be up to the FAA’s Aeromedical Division in Oklahoma City to make that determination, not a DME. It is most likely going to be an uphill battle and may result in a denial as requiring the use of an anti-psychotic prescription medication while assuming PIC duties almost always is.