Welcome to Just Answer and thanks for your question.
Do you have a copy of your birth certificate? That should list your biological father's name. There is no delicate way to say this, but if your mother was sexually active with many different men around the time you were conceived, it is possible that she really doesn't know who your father was. In that case, perhaps she can narrow down the list of suspects and you can have DNA testing done but that is going to require the consent of each man. It's also possible she was raped and the culprit was never found. In that case there is nothing you can do.
Please let me know if you have questions.
No, just knowing your own DNA doesn't do anything to identify your father. To make an identity, you would need to have a suspected father's DNA to compare it with. If enough exact matches are found in the two DNA samples, that is how paternity is established.
I'm sorry that you can't learn the identity of your biological father, but if your mother doesn't know who he is, then no one does.