What structure you injured exactly is very difficult to identify over the internet, but I don’t think it will wildly change your approach to managing the problem.

1) Don’t do stuff that makes it hurt. Don’t do stuff that makes it hurt LATER. If you’ve injured a muscle, you have to really baby that sucker for the first few days if you want it to heal. New muscle tissue being laid down is really vulnerable. I would honestly play it pretty chill for a week, then start experimenting with re-implementing training and seeing what you can do that doesn’t irritate it. Use the painful movements you are currently aware of as clues.

2) Get your front rack on point before you resume working on power cleans. If you don’t have the position to perform the movement, it’s nothing but a liability to you. You’re likely just going to keep stressing the soft tissues of your hand and wrist until you do. Mobility WOD has a ton of content available on how to earn this position.

Do not let your impatience to train trick you into pushing your luck. If you do not treat the injury well now, it’s just going to turn into a long-term battle for you. A week or two of training is a drop in the bucket compared to the rest of your life.