Baby trying to drop??

Does everyone drop before labor? I know the uterus is supposed to drop, not the baby itself but I think I can physically feel my daughter wedging her head further into my pelvis. She does it all night every night for past two days, like I'm afraid to push too hard during a bowel movement because I think she'll fall out. It hurts so fucking bad, like lightening crotch but x100 + extra pelvic pressure. I can even feel her little legs push against my ribs while she's wedging herself down there. I'm 36 weeks today. IS THIS NORMAL?