What should I do?!

FTM- I'm due July 22nd. The baby has always measured 1-2 weeks ahead and my family and husband's family is known for big babies (i.e. my brother was born at 36w2d and weighed 8lbs 14oz and my mom had no medical issues but they induced her bc he was getting so big).

Yesterday at my 38w appointment My doctor said I'm thinned, softened and 1 cm dilated (same at 37 weeks) but my cervix is still high (idk what that means or how to get it "lower") so she said she can't do a membrane sweep because she can't get to it and she wont schedule an induction date. I'm honestly afraid this baby is gonna be too big to birth vaginally if she lets me go to 41/42 weeks and i reallyyyy do not want a c-section.

I really don't know what to do or if there's even anything i can do. I started walking the neighborhood yesterday because that's what she advised for me to do. But I'm at a loss 😫 why won't she induce me??

🛑I know that babies will come when they are ready and all that so please don't come at me with it.