2000 Cavalier Automatic Transmission won't shift from 2nd to 3rd

Recently replaced a blown engine in my 2000 2.2 automatic Chevrolet Cavalier. Now I have a practically new engine (35k) that purrs like a kitten as long as you don't attempt to go past 2nd gear. It will not shift into 3rd. The mechanic who replaced the engine said that this was most likely the cause of the blown engine in the first place.

What could be causing the engine to shift in the first 2 gears, but not into the 3rd (and beyond)? And what would be the cost to repair/rebuild/ or replace the transmission?
This is driving me nuts as I just put alot of money into getting the engine in only to find this problem!