This almost certainly has something to do with how you're racking it rather than how you're dropping it. Unfortunately, I can't tell how you're racking it from here.
My wrist hurts like hell after I do power cleans. Imagine karate chopping a block; the part of your wrist that would contact the block is where the pain is. Relevant info: I can't drop the weights from rack to floor--no bumper plates. I have to drop them from the rack position down to the top of the deadlift position, and then set them down. I try to let my thighs absorb most of the impact. Does the way I drop the weights have anything to do with the injury? I have no clue. Also, it's only 185 pounds, so I didn't think I could hurt myself with that little amount of weight.
This almost certainly has something to do with how you're racking it rather than how you're dropping it. Unfortunately, I can't tell how you're racking it from here.
If you catch the bar in the rack position essentially with your index and middle finger on the bar (the bar will be right up against your throat) as opposed to keeping all your fingers wrapped around the bar, this should alleviate the pain you get. I had the same issue going on, especially after switching to the hook grip, but once my confidence improved with having the bar in just my index and middle finger, all my wrist pain (discomfort) stopped.
Sounds like stretching would help.
Load up a bar in the rack with something very heavy. Get under it in the front rack position. Get a friend to push your elbows up as high as possible. Repeat as necessary.
A couple of things:
1) finger and wrist stretching
2) you're getting to a weight where tape or wraps might not be a bad idea.
3) like gzt said - maybe a video would be appropriate before you really hurt something. No point in being unable to train tomorrow.
Thanks for all the responses. I did power cleans today, after reading this article quoting Charles Staley on correct form. Specifically, the "elbows out" & shoulder blades retracted cues. Worked like a charm. No pain.