Hello and welcome to justanswer. I am David and I will be assisting you with your transmission problem.
Is the check engine light coming on when you experience these problems? Does the transmission stay stuck in 2nd gear, or does it try to shift into 3rd and slip like it is in neutral?
The problem you are experiencing is most likely due to a sticking 2-3 shift valve in the transmission valve body. Flushing the transmission will not fix this problem. My suggestion is to remove the transmission pan and the 2-3 shift solenoid. Remove the valve from behind the solenoid and clean the valve and the bore. You can even polish the valve with some 1500 grit sandpaper, then wash the valve with brake cleaner. Coat the valve with clean transmission fluid before reinserting it and checking for smooth movement in the bore. It is not a bad idea to go ahead and install a new shift solenoid at this time as well.