Transmission or Engine?

I have a 97' Pontiac Grand Am w/ 120,000mi. On it. In June of this year, I was driving it from Colorado to Georgia because of moving. Halfway through Kansas, the car could barely go up hills. You could only get it up if you pushed the gas all the way down and the needle would go all the way to red. So I took it in and was told that the 1, 2, 3 gear were fried and the 4 & 5 were on there way. I had the whole transmission replaced. When I got it to Georgia, I had to take the car in to get checked out to start the warranty. The Pontiac people said that my 1 & 2 gear were slipping. So I took it into a shop that would honor the warranty and they said they found nothing wrong. Well a couple of weeks ago, I started noticing that when ever I excelerated out of a turn or going up a hill, it felt like the 1st gear would hesitate going into 2nd and then I would have to press harder on the gas to make it go and it would lung into gear. I took my car into the same shop to honor the warranty and they said they found nothing wrong w/ the transmission again but it looked as if I was only firing on 5 cylinders. They drove my car to another place, who ran a diagnostics and said that I would have to replace all my coils, plugs and wires. They did it and I got my car back yesterday but when I excelerated out of a turn and tried to go up the small hill to my carport, I felt the same hesitation. Please help! Is it my transmission or my engine and if so. What's wrong. Also for the past 6 months, I have been hearing knocking sounds coming from the rear of my car when driving and in idle. My father says it may be the Universal Joint. Again. Please help. What is going on w/ my car?

Thanks.