Schizophrenia and obsessive thinking, which is a symptom of obsessive-compulsive disorder (OCD), rarely present together (although there is a noticeable comorbidity between schizophrenia and OCD). However, I do not have OCD and my schizophrenia symptoms never included obsessive thoughts.
At least not until I was put on an antipsychotic medication with a rare side effect of causing obsessive thoughts. Then, not only did I have to deal with symptoms like hearing voices, but my generalized anxiety disorder morphed into a deep well of obsessive thinking with no bottom. Schizophrenia and obsessive thinking is a tough pair to deal with.