When your car jerks when the transmission is changing gears it's likely due to either low transmission fluid, clogged transmission filter or it could also be a sign that your transmission fluid needs changed.
If your transmission fluid is good and the transmission is not low on fluid and the car still jerks when the transmission shifts then you should take the car to a mechanic or a dedicated transmission shop to have them diagnose the transmission.
It could mean that your transmission may need rebuilding or replaced. Or it could be a bad transmission fluid pump that is about to go out.