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Welcome to Just Answer and thanks for the question. No doubt this was a traumatic event for your brother, but if 3-4 tests have all been negative, he doesn't have syphilis and hasn't been misdiagnosed. Syphilis tests are far more likely to give a false positive report than a false negative one. He needs to contact a mental health professional about his post traumatic stress disorder.
Those symptoms can come from a variety of things from alopecia areata (an autoimmune disorder that leads to loss of all body hair) to a common cold. The botXXXXX XXXXXne is that his beliefs are irrational and dictated by his mental illness (schizophrenia) and stress. It is difficult to reason with people who will not hear the truth. I know you are terribly concerned. i would be too if it were my brother, but other than prodding him gently in the right direction, you can't really be responsible for what he thinks and does. It is always heartbreaking for the families.
It is only in the earliest stages of the disease that you get a false negative with a syphilis test (the first couple of months after exposure). If he was raped 4 years ago, and today has a negative test, that means that he doesn't have syphilis currently and has never been exposed to syphilis because he has no antibodies to it. Even if it were syphilis, it is curable with an injection of Benzathine penicillin G once a week for 3 weeks. The problem is that no doctor is likely to order shots for someone who doesn't have the disease in the first place.
Your local Health Department is a good place to start for a face-to-face chat. Some towns also have STD clinics. You can also check below: