What would make the transmission whine like a power steering pump. 97 lumina 3.1

What is your question?

I think it overheated because I was doing a lot of driving that day it was slipping on hills an when I would make a turn it felt like the axles weren't grabbing sort of shuddering the fluid is burnt and brownish when I checked it but.it sounded like pressure in the thermostat idk if that would affect it if it was stuck open or closed. The fluid also seemed a little high I added a quart after I did an axle swap

What makes this problem better or worse?

It seems to drive better in higher gears but won't down shift with pedal down

How long has your 1997 Chevrolet Lumina had this problem?

Few days