Please need help with the dukes archive area

So I am in the dukes archive area and I got passed seath but I got to the part where you need to drop down onto the rotating staircase and after I activated the switch that turned it I died and now every tins I go back there i see that the staircase is rotated the wrong way. Is there any other way to get to the crystal caves or am I screwed

Both staircases in the area spin together so you should be able to now access the other area without issues?

Yup, as Fex said both stair cases turn when one's lever is pulled. So if you need the first staircase to be facing the other way, just run down the hallway and turn the second (or vice versa if need be)