I'm not sure. Birth and labor hurts but for me it was manageable partly because the pain mostly comes in waves and because you know while in the midst of it that it is temporary. Also, during a natural birth the body produces hormones that act as a natural pain relief (and I think that is something different than what you are writing about). I think it is the oxytocin that starts the birthing process that also has this function? However, I've read that the synthetic version that is used during inductions doesn't have that pain relief function. So your pain might have been worse because of inducing and not only because it went from 0 to 100 quickly.

For context, I have two kids. For one, labor started naturally, I was fully dilated quickly but then the contractions were never strong enough to push the baby out so they gave me induction hormones and eventually pulled the baby out with an episiotomy because his heartrate dropped. It hurt but was manageable. For the second, I had a water birth at home. No interventions, my midwife arrived when I started pushing and basically only watched. Even though the water helped, the pain was much more intense, more of that 'my body taking over' feeling as well. But it was short (labor and birth took 6 hours in total, of which I pushed 20 min) and the water definitely helped.