Transmission problem in 2001 buick lesabre

have transmission trouble in 2001 buick lesabre. bought car new. has 56000 miles on it.only drive about4000 miles per yr. since now age 73.
Here is the problem. If I drive car for 30 minutes , it shifts ok. After about 30 minutes of driving, the shifts from 1st to 2nd, and 2nd to 3rd hit hard, like a thump noise. There is no grinding of the gears in shifting. There is no delay in shifts.Here is the weird part . If I then stop the car and let it rest for half an hour and then restart and drive, it shifts smoothly again. When it starts to hit hard between shifts, there is a whinning sound that accompanies this. The manuel that came with the car says to change transmission fluid and filter at 50000 miles if its been all city driving. Its 90 percent city driving. Have not changed fluid or filter, as it may not be the problem. if I bring car to a transmission shop , they will probably tell me to rebuild transmission. I wont do that since car is 12 years old. If its a small repair under 200 dollars, id fix it. Any transmission experts out there who might know what the problem could be?
thanks much if you could reply to this question.

If this were my car, I’d do a proper transmission service, drop the pan, change the fluid & filter, cross my fingers and hope for the best.

If you later determine the transmisson is kaput, and you decide to sell it, I’ll bet there is a teenager in your neighborhood who’d like to buy this car from you on the cheap. Might get you some good karma. Best of luck.

It should have been changed at 30K so you’d already be due for a second fluid change pretty quick. Tell the trans shop and have them check the pressures and check for codes and have it serviced. It could be just low on fluid.

You will never find out if there’s anything at all wrong until you do the basic maintenance.