I doubt very much that the screeching you describe is from hydraulics. Automatic transmissions are not supposed to make any noise and if they do, it is usually associated with the various rotating elements. Please clarify something... is the noise only occurring when you manually shift from 1 to 2 and 2 to 3? In other words, when you put the transmission in "Drive" and the transmission upshifts on its' own, does it still make the noise? This is important because there is a difference between 1st gear while in "LOW" vs 1st gear while in "DRIVE". Different components are locked/unlocked and it may be the key to your noise. My first guess is that you might have a noisy/slipping low/reverse sprag.
