But obviously, the circumstances of your conception and birth are very emotionally painful for your birth mother.
Your birth mother has made it clear to you, it appears, that she doesn't want to discuss this with you. And while I understand your issues, you need to respect her feelings. She may change her mind. She may not. There's no way to know.
There may also be a question of paternity. Perhaps your mother doesn't want to tell you because she is not sure of who the father is, or you were conceived under unpleasant circumstances. Maybe she is trying to protect you because she doesn't want you exposed to him. Maybe he was married. There could be all sorts of reasons.
The best thing for you to do at this point is to go to Ancestry.com and find out about purchasing a DNA kit. It will tell you what your ancestry consists of, and will link you to people that you are genentically related to.