Head down v/s engaged

I am 37.1 days and my belly is still high up i am having hard time breathing . My doctor says babys head down and  in ultrasound it was written baby in cephalic position but i was wondering when actual engaging happens? I mean have you Ladies belly dropped if yes when does that usually happens? I mean i want to have normal delivery vaginal birth i mean i  scared if baby doesnt dropped wil. They do c section?! I dont have any idea how these things work i am a ftm share your thoughts with me