During the last snow storm, I ended up getting stuck a few times. It was late night and I wasn't sure if anyone would come around to help me, so I had to spin my wheels to free myself. Since that night, my transmission has been very loud (whine) at idle, even louder in reverse, but decreases with speed to the point that it becomes unnoticeable at around 3000-3500 rpm. Other than the bothersome noise (and it does shift kind of hard when going from park to drive or reverse, but has been since I bought the car) there are no other issues. I've checked the automatic transmission fluid and noticed it was dark with what appeared to be very fine metal. What is the probable cause, and how much will it cost to get fixed?

mileage - 135,000
4spd Auto