96 GP 3.4 transmission problems

I was driving back to michigan from new york yesterday. Towards the end of the trip I noticed it chugging on me. I thought it was a misfire. Wasn't bad, just now and then. Stopped for bathroom break, then 20 miles later stopped for gas. Got back on the expressway, got up to about 40 mph and it acted like it shifted into neutral. RPMs shot way up. Stopped on the shoulder, but couldn't take off again. Seemed like I was in neutral. Shut the car off for about 30 seconds, started it and it took right off. drove for about 15 to 20 seconds and like it popped into neutral. I got it to a parking lot by starting it and driving it until it seemed to jump out of gear, put it in neutral and shut the car off and coasted for about 20 seconds. started it and hit drive again. It would drive for 15 to 20 seconds and same thing. Took me a while but got to a parking lot. Added tranny fluid, and it was full. Still does the same thing. Is the tranny shot or do I have a sensor or something gone?? Thanks for any help.

First step would be to check for transmission codes...

Car is still in a parking lot 45 miles away. Getting a car dolly this weekend to get it home. Now when you say check for transmission codes are you saying the OBD II and get the code?? The check engine light DID come on once and once only, so hopefully it recorded a code. The car is equipped with the second gear start, which I had no clue what that was when I got it until I read the manual. I had never heard or seen of that before. I even tried using that when it did this. No difference. I read there is something that electronicly controls the shifting, so maybe it isn't the transmission after all. I'll know more when I get it home and can look at it. Stranded in a grocery store parking lot at night 45 miles from home isn't the perfect place to look at it, LOL. Thanks for your help I will let you know anything I find out. If anyone has any other thoughts or suggestions I welcome them with thanks in advance.

Unfortunately your transmission is probably shot. I'm sure it's plugging the filter thats why when you shut it off it moved again for a short distance.

Decided not to even mess with it. Went out and bought a 2013 Malibu, no more wrenching on my cars, LOL. Thanks for the help guys.