Is my transmission dying? When I drive it for long periods of time it acts like it is about to die when I idle?

It shakes a lot when I stop, like it is pulling back in forth. Then when I put it in neutral while Idling it stops. I also have a problem of going up steep hills, I have to push the gas pedal all the way to the back just for it to go up, but it doesnt make it to the speed limit. It is a 90' ford probe so it is pretty old. I checked the fluid levels and everything seems fine.