i'm so sorry. My grandparents all died by the time i was 19, way b4 i got pregnant last year at 24, but i know it was very hard for me to lose my grandma, the only one left I had, at 19. I knew of someone whose mom died 2 weeks after her daughter's birth. also, if it helps any, my grandma and I have the same birthday, so whenever my b-day comes around, I think of her and how I miss her. my grandfather died on my 3rd birthday, which I remember that being the worst b-day ever for me. my mom was crying so much that day and i really didnt understand why at the time.
i think just try to realize your grandma's death day and child's birthday are not connected; even though their the same day, see them as 2 separate things, dont bunch them together. Give yourself the allowance to mourn, cry in private if you have to, dont try to avoid mounring.
remember, due dates are almost always off, so they may not share the same exact date, if that helps any. I know it will be hard to lose a grandparent so close to just giving birth to a new child. also, i hope this helps, but your grandmother has sort of "put her time under earth in', she has lived a long and probably fulfilling life, became a wife, mother, grandmother, etc. Now her time has come, while your child's time is just beginning, its the cycle of life.