What happens if my baby comes early?

Shelby
I'm supposed to have a C-Section @ 39+1 (nov 25th). I'm scared to death to delivery vaginally for reasons I'd prefer to keep private. I was also diagnosed with seizures and I'm anemic so my Dr has agreed to do the procedure for my health both mentally and physically.
But what happens if I go into labor early? 
(I was supposed to be a cesarean baby but came rushing out of my mom before the procedure)
I'm 35+6 right now and have been having contractions for weeks but so far no dilation just effacing and babys stationing but it still makes me nervous because of how fast my mom went from closed to 10.
Also would the reaction of what the Drs would do change depending on how many weeks I am?
Any information / experience is greatly appreciated. Thank you for your time.

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