I didn't have ligtning crotch but definitely a lot of pressure on my pelvic area from the baby's weight. I couldn't tell when my baby was engaged but my gynae picked it up during ultrasound at around 35-36 weeks. Babies can engage as early as 34-36 weeks for first time mums but it's not definitive of impending labour. I didnt deliver until w39+6 though my baby engaged early.
I also had vagina pain during 3rd trimester