Stress and Worried Father 😨😕😨

I am soon to be a father. I am excited ! However my excitement is often mixed with stress and worries because of the relationship status w/ my baby's mother. Recently she has been becoming more and more distance with me. Currently we are on a "break" because of her request. 
She is 20 weeks.  I want to be apart of every moment of my child life from the beginning - but I feel like my girlfriend will not let me do so ! 
We currently live about 5hrs away. However, plan to live in the same city when the baby get here.
She has limited communications with me because she said I am too needy - because I call and ask about the baby and how her day is going. I like to read to the baby over the phone and love to hear how the baby is moving through out the date. I still care and love for the baby's mother - however I don't think she feel the same. 
I feel like I will have not say in the life of my child. I feel she will only allow me to be a figurative person in the child life - and the more I read about court order custody order - it seems the court will do the same to me. When I try to call her - the conversation make it seems like I am a burden for her - and then after I read to the baby - she always say " that's all you have to say".
I need to vent because everyday I stress out about this. ould like to get your input how I can overcome this stress and worry. Or if you know anyone else who has experience this .Â