Assuming your form is good, you’re probably deadlifting too often or doing too much in one session.
Usually get Deadlift DOMS in my high Erector Spinae or Glutes.
Do something easy like the seated leg press if you’re to sore too squat/lunge or Deadlift anymore, that’s the only time I use it.
By back is really stiff for a couple of days after maxing. Is this happening to others?