Hi there, I'm 35 weeks pregnant and a first time mum too and know how you are feeling. A midwife said something to me that helped me so much with the anxiety of giving birth. She said that I should remember that my body knew exactly how to get pregnant and got me so far without me doing anything, and that I should trust and have faith that it will know how and what to do when the time has come to give birth.
Hope this helps you too.
And it's very helpful as well to talk to ppl how know about this, so if you have a chance to join a class i would highly recommend it. :)