@Icon,
I see no reason why you should not be permitted to date just because you have a mental illness. Mental illness is something that in some form or another affects millions of people or more worldwide. Most of these lead normal lives, including having a romantic relationship with another.
I do agree that if you decided to pursue a longer-term relationship with a woman you would need to inform her of your condition, but under no circumstances should you inform anyone you are casually dating. This is counterproductive because unfortunately most women would probably not understand and go no further with you. Telling someone you have schizophrenia is definitely not something to do on a first date.
Schizophrenia is a widely misunderstood illness, perhaps the least understood of the mental illnesses by the general public. Many people do not realize that in today's society schizophrenia is easily treated, and that most people with the condition live fulfilling lives.
If you are not receiving treatment, that would be the first step before pursuing activities such as dating. But I suspect that you are since you know you have schizophrenia. Someone with schizophrenia who was untreated would be very unlikely to recognize his condition.
If you are on the right treatment you should not have to worry about having psychotic episodes. If you are still having psychotic episodes, you and your doctor need to consider a different treatment.
Ideally two people with schizophrenia would not become life partners, or at least not have children if they do, because they would almost guarantee the child would also develop schizophrenia. But if you have no ethical concerns over this possibility, then someone else with schizophrenia may be an option for you.
Do not limit yourself and what you can accomplish just because you happen to have a condition that is beyond your control. You are entitled to happiness and success just the same as any other person is.