A very difficult shot to pull off, so don't feel too bad. The blown sky is one of the issues that would have been quite hard to overcome. I'm not even quite sure how you'd do it. Does the tree seem to you like it's ready to fall to the right? I get that feeling and don't know if it's just me or the crop or what.
The mist probably limited you a bit too. I'm guessing it wasn't falling "down", but rather floating around. Had the drops been more like rain and falling, I would have tried a longer shutter speed to add some motion blur. The horizontal sun rays and vertical rain blurs may have been cool.
Don't sweat it too much. You really did take on a hard, hard shot.
EDIT: after reading the other comments, they did a better job of relating that the mist doesn't quite look like rain and confused people. I was getting at that in my paragraph above...
I can't figure out if that is rain in the sun streaks or if it's just grainy from excessive dodging. That's the only place it seems to have that texture. I think it is way overexposed and if anything, most of the right side should have had some burning done if that was allowed in a basic editing challenge at all.
Sorry, I cannot perceive rain in this shot. It may be there, it just isn't evident enough. The bottom right is blown and there is a lot of noise (rain?) on the whole right side.