Great question, although I am sorry to hear you have been frustrated to this level in the past. It is rough to have family members who have mental health issues, especially if you feel constantly rejected by them. But to answer your question directly, yes, schizophrenics are always saddled with poor social skills. Technically, there is a constellation of symptoms called "negative symptoms," which are not nearly as noticeable as the "positive symptoms," which include the more classically-recognized hallucinations and delusions. Negative symptoms include poor hygiene, social withdrawal, and inappropriate emotionality. Between the three of these, you can imagine that social interactions are going to be strained, or perhaps even impossible. At the very least, they are going to be frustrating and alienating to the person trying to bond with them, so it does not surprise me that you have had your experiences with your family members.
The other problem is that the medication does wonders to curb the positive symptoms, but does less to treat the negative symptoms. Sometimes psychotherapy can help these, but I fear you are going to always feel saddened by a lack or true emotional connection. I wish you well... If you are satisfied with the response, please hit "Accept." That is the only way I can receive credit for my answer. Thanks-