2002 Pontiac Grand Prix Car Shifting

I have a 2002 Pontiac Grand Prix GT with about 127.5k miles on it. My problem with the vehicle is that when I drive it, it shifts and rides really smooth, but once the car has warmed up and I have been driving it for awhile, the shifting becomes less smooth and then starts shifting harshly and the car jerks really badly. But if I go faster than about 55-65 mph, I feel no harsh shifting at all. I drove the car a good ways from when where I bought it (about 2 hours) and had no problems going high speeds. But when I go the regular speed limit, it started shifting harsh and the car would jerk really badly. I took the car the next day to get the transmission fluid flushed and serviced, but the problem continued. I took to get a diagnostic ran on it and the transmission shop told me to just go and get it rebuilt, but they want $2150 at least. I been researching the problem and reading what people who have similar symptoms with their car, and the answer I kept seeing was that the transmission solenoid was bad or the pressure lines weren't good. I been told it could be a number of things like a bad fuel injector, bad torque converter, any number of problems ranging from minor to major. I'm a college student and the car gets me to school and back without the harsh jerking, (and my theory behind that is because I get on the highway and interstate and go 65-75 mph the whole, not having to shift from the first couple of gears) but in city limits, I can't even go down the street and back without it jerking and shifting irregularly, sometimes subtle, sometimes harsh depending on the distance I go. I feel as if the problem is in its early stages and only one part of the system needs to be fixed as opposed to the whole tranny, but if I can't figure out the problem and solve it, I will eventually have to rebuild or purchase a new transmission. I am really hoping to get this problem solved and hopefully not have to resort to having the tranny rebuilt because its too costly for a college student. I know repairs aren't cheap, but I'm hoping its cheaper than $2000. I'm not too knowledgeable about cars, and I'm hoping to get advice from a professional who doesn't gain $2000 from my poor understanding of cars. Other than the rough shifting, I feel if I get the car fixed, it will last me for a long time.