Car jerks when changing gears

Sadly, this very likely can only be diagnosed by a mechanic who experiences the condition --unless it can be immediately reproduced by said mechanic. And it would be helpful to know the year and whether it is an automatic or manual or if you have any error codes. The following site suggests 13 different possilble causes: https://www.repairsmith.com/blog/transmission-jerks/

I am not sure of the list includes the possibility of bad coils.

The information offered is a little slim to narrow the problem down.

When you say it "jerks," this description could fit several actual symptoms. If by "jerks" you mean the engine misfires, it could be caused by the need for a major tune-up (including plug wires and distributor cap), or it could be a problem with fuel delivery, contaminated fuel, or defective components in the fuel system.
I assume the CHECK ENGINE light is on (and has probably been illuminated for some time now). Begin by doing a readout of the stored codes, and use the results to begin your diagnosis.
If by "jerks" you mean the transmission is slipping (engine revs but car slows down or doesn't accelerate), you have a transmission issue. If the transmission fluid and strainer/filter have not been replaced within the past 5 years or 50,000 miles, have a complete transmission service performed.
If by "jerks" you mean that the steering wheel wobbles or pulls, you have a problem with the front suspension.
If by "jerks" you mean that the car shudders or pulls when you apply the brakes, you need brake work.
I think I covered all of the "jerks." ;)

You may need a tune up . When was the last time you changed plug wires and had a decent tune up that will cause a vehicle to jerk when reaching higher gears the more strain on the engine the more it will jerk!!!

probably needs an overhaul. jerk the car forward and backward a few times or try cranking it to change its position. drain the oil and see if its got metal shavings in it.

It wil require that your trans is rebuilt or replaced
with a factory built or reman

If you change your fluid every 3 years you avoid
most trans problems

After 12 years they are pretty much worn out anyway

most likely its your distributor cap. if its old it means its worn out and water will get into the cap and cross wires, which makes one of the spark plugs skip. replace your distributor cap and rotor.

That can be a mount, but you would of said it jerks at all time from park to drive and when your driving. and also reverse.Going from park to drive is there a pause and do you hear a buzz noise then a gear change. If you did that would be the solenoid. So here it is from park to drive and the RPM is in range this is known also as a harsh up shift, it is mechanical in nature the clutch pack is taking more pressure than it need to achieve a gear change. In other word your transmission is mechanically worn

theres most likely a bad sensor located somewhere on the transmission.

Sounds like the band that controls 3rd and forth gear is almost worn out. Have you followed the recomended interval for transmission fluid changes? What does your trans fluid look like?

You Think your mechanic did not Connect your distributor cables.