Hi Chong. My daughter had similar experiences. At about the age of 4, it was mentioned that her interaction with other children was a slight concern, but that she would probably grow out of it. By the time she was about 10, she was seeing a psychologist for her symptoms: social anxiety and elective mutism. The psychologist wouldn't commit to any specific diagnosis, as at that age, the body and mind are changing so much.
From about the age of 11 she started saying that other girls were talking about her i.e. she was hearing voices although we didn't know it at the time. When she was 14, after a family outing during which she was hearing voices in other cars, we decided to take her to a psychiatrist. After several months of deliberating, the psychiatrists decided she had sz. But it took them a long time to commit to the diagnosis, again because during puberty the mind is changing considerably and it's very difficult to decide on the correct diagnosis. The diagnosis is life changing so the last thing you want is for your child to be treated with antipsychotic drugs, because of a wrong diagnosis.
With paranoid sz, logic has little effect as their minds will very cleverly counteract the logic. You can try it, but be prepared for it to escalate and get very frustrating. In our experience with sz, the illness comes and goes in waves, whether our daughter is on medication or not. However, the waves are much much bigger and more frightening/dangerous without medication.
May I ask how old your daughter is Chong?