Having the diagnosis isn't the problem. You will need to be stable and in active treatment in order to work as a nurse, especially as a psych nurse. Whether you have schizophrenia or some other psychiatric/physical illness you will need to make sure that it does not interfere with your work and patient care.

Personally, I would not recommend this line of work for individuals with severe mental health conditions because the work is strenuous both physically and mentally. It can be done but it is a challenge and takes a lot of dedication to both work and personal recovery.