Whirring noise under hood loud when engine turns on but whirring becomes lower when driving

It could be a belt. I recommend that you do check all fluids. When you get stuck and spin the tires, you can lose trans fluid. Also, you mentioned that it overheated, make sure the fan is working properly. THe idea that it overheated makes me think perhaps the fan wasn't working properly. Start the car, open the hood and allow it to warm up in park. See if the fan comes on when it should and that it is spinning at a normal speed. You may have a bad bearing in one of the fans making the noise. One last thing, and I have to be honest, I don't think it's related to getting stuck, the water pump can make a whirring noise if the bearing is going bad. I do recommend checking all fluids too.

Let me know if you have other questions.

Joe

The trans fluid should be checked when the engine is warm, running, and the transmission is in park. Check the dipstick closely. Some have a steel clip that raps up and around to hold it in place. Other than that, is should slid out.