1997 Pontiac Sunfire Car won't back up, please help!

OK this is really strange, and I'm hoping that somebody you there has heard of this before. (I have a 97 2.2 sunfire)

when I try to put the car into reverse, the 3 speed auto tranny catches right away. I can tell it's in reverse. BUT. The car will not back up at all, in fact it feels like I'm trying to drive with my foot on the breaks, or I'm backing up into a brick wall.

here's another strange thing, when it does that, even putting the car into neutral does not free it up to go backwards. The car always seem to be OK in forward gears, but the wheels lack the ability to spin in a backwards direction at all.

When it does that, I can usually drive forward for a bit, and then try R again, and it will give me reverse, but I'm sick of having to back into every parking space!

fluid level is fine, and the fluid does not look burned. No check engine lights are on


I'd take it to a transmission shop, but it doesn't do it every time, and I'd like to see see if anybody else has experienced this problem before I play "hit and Miss" with them.

I'm assuming it's a transmission problem, but I could also see how the brakes could be locking up, or even a drive Axle problem.

thanks for any help you can offer.