When attempting to accelerate engine revs high car does not move, transmission not shifting properly

I took off from a red light and the car revved up to 6,000 rpm's and would of kept going if I let it, but I heard some noises and it revved real high. I put the car into neutral after I realized it would not accelerate at all. So when I put it in neutral and then back to drive I heard something click. I hit the gas and it drove, so I tried to get back on highway and when I accelerated hard and put a lot of stress on the engine it revs up high and will not shift. Now if I drive very easy like very normal and not try to get on the car at all it drives somewhat okay. Until I hit the gas hard it will rev up high and I will have to let it rev down and then put into neutral and then to drive again to get it to go. This just started three days ago.