Is it possible to have schizophrenia without hearing voices?

Yes: Symptoms can vary depending on the type of schizophrenia. Some may hear voices, believe others are controlling their minds, are paranoid (i.e. The fbi is following them) and have disorganized thoughts. This link provides some general education about the illness that may be helpful for you: http://www.Nimh.Nih.Gov/health/topics/schizo.

Yes: By definition, schizophrenia is about psychosis. Psychosis means the patient is getting external stimuli from the environment through one or more of his or her five senses, that does not objectively exist. In other words there are auditory,visual, olfactory, gustatory, and tactile hallucinations that can be experienced by the patient. Auditory hallucinations, however, are the most common.