From my experience, Power-steering pumps and Water-pumps usually squeal, b/c of bearings losing there outer coating through wear and tear. But, rack and pinion will whine especially if you turn the wheel all of the way to the left and to right.
O.p. check your Transmission's fluid level and keep track on hard shifting is about all you can do. Unless you can tear apart you cars auto-transmission and put it back yourself.
Honestly, it sounds as if your Auto is gonna give sometime in the very near future. Sounds as if the pinions and such gears are grinding ever so lightly, just enough to indicate wear. So, wide-open throttle pulls are not good your auto as we speak especially if it only does that at such time.
Time for an Auto rebuild.