My adopted daughter birth father is unknown. I was a single mother and one of my male friends became her psychological Dad. He's distant in his relationship with her now that she's an adult. She feels sad but has had the opportunity over the years to adapt and adjust.
I sympathize with you. You have lots of reasons to feel sad and more. I suggest that the reasons for such strong emotions isn't so much that you don't have a Dad but that there are several issues surrounding that. I suggest you look closely at those issues. First make a list of all the things about not having your Dad that bother you. You do have a Dad by the way. You just don't know him. Then take each issue and see if you can find a way to resolve it.
For instance, you're angry that your Dad and his family have made no effort to contact you. You don't know why. Perhaps they don't know about you. Perhaps your mother told them to never contact you. Perhaps they don't know you want to be contacted. Perhaps they're afraid to upset their own lives. Perhaps their own lives are not going so well. ETC!
Yes, it hurts to not have a Dad in the usual sense of the word. Many women don't have Dads. My granddaughter has a Dad but he lives in a different state is not sensitive to her needs to have him in her life. She does talk about and write about her Dad during those days at school and with friends when having a Dad is important but she has to tell stories that are for the most part untrue.
My granddaughter has a step-father which does help a lot. But she still misses her Dad. And it's taken years for my daughter to work thru the issues surrounding not knowing who her birth father is and having a stand in Dad who isn't available. She has a 2 month old baby that her "Dad" hasn't been to see even tho he lives a mile from her. Sad!