It has to be a C4 or a C5, a C6 will not fit without major tranny tunnel alterations in a fox bodied car.
The C4 I stuck in the boys 89 mustang wasnt right either, it did something similar, I had to pull it and get a total rebuild, C4 rebuilds are cheap if you pull it yourself that is.
If I remember I paid $350 with a remaned converter.
You can try the fluid and filter deal but chances are if its slipping your tranny is toast, C4's have a tiny oil pan, doenst take much to smoke one.
Make dam sure you have manifold vacuum hooked up to the modulator when you get it back in, leaving it off will smoke one pretty quick if your putting any kind of power to it.
Goodluck, Cp