Q: What's wrong with my car?

About two weeks ago my car would jerk sometimes but drive normal, and then a week ago the car wouldn't go when i would stop at stop lights or stop signs and i would have to stomp on the gas for it to start going and then it would start going really slow when i'm stomping on the gas, it would go very slow at like 5 miles per hour max or 10 mph and when we were just driving around my neighborhood the car went from 7 mph to about 40 mph by itself without my foot on the gas and the brake wouldn't stop it, the car would slow down and then randomly start speeding very fast on small streets, we couldn't stop until the car was starting to go 5 mph again when we were driving back home and we had to shut off the engine for the car to stop, my brother had told me it was the speed sensor in the transmission but when i took it to a nissan dealership they said it was the whole transmission and we're going to charge me $4000,please help me

My car has 88000 miles.
My car has an automatic transmission.