99 GP GT shift problem. Please help ASAP.

I have a 99 GP GT. It started acting up recently and I don't know what the problem is. When I first start the car and put it in gear and drive normally, the tranny shifts smoothly. It will continue to shift smoothly until I really put it to the floor. It seems that as soon as I drive at higher RPM's, when the car shifts (into any gear) the tranny will shutter into gear, doesn't feel like a slip, but shutter is the best word I can think of to use, maybe shake would be a better word. Anyway, upon slowing down to a stop and then starting again in 1st, no matter how low or high the RPM's, when the car shifts it doesn't shutter anymore, now it really slams into gear hard. Like I said, it then happens in each subsequent upshift into all the gears. If I stop and don't drive the car for awhile and then get back in and drive, it shifts smoothly again until I really step it down and hit higher RPM's and then it starts to slam into each subsequent gear again. Please help me with this, does it sound like a tranny problem or computer problem or what?

How many miles do you have on your car? My GTP had same trouble. Thought the trans was going to come up thru the hood. Changed filter, the trouble stoped.
Hope it helps you