Is my ex schizophrenic

I am needing to know if my ex boyfriend and the father of my son schizophrenic. When we were dating, he felt as though people were watching him and that his family was in on it. He would question me obsessively about whether or not I loved him and if I was cheating on him. He has extreme highs and lows and seems to be unable to handle small situations. Yesterday when he came to pick up our son he was struggling to form complete sentences, and wasn't making any sense. I would tell him that he wasn't making sense and he would shake his head and say I know I am sorry, but he would stop making sense seconds later again. He was staring at my current boyfriend in a very weird way, not in a confrontational way, just staring. At one point he was watching my current boyfriend and his friend conversing and would start talking as if they were talking to him and then would shake his head back and forth and mumble to himself. The weirdest part was that their backs were to him and he was far enough away I don't think he could even understand what they were saying. When I asked if he was ok since he was talking to himself he laughed and said yeah I see dead people. I looked at him confused and he laughed awkwardly and walked away. He sleeps all of the time, has struggled to keep a job, is very lazy and always seems to say the wrong thing at the wrong time. It is almost comparable to a child because he doesn't seem to understand what is appropriate to say in social situations. I am beginning to worry about the safety of my son.