I had a feeling it was a Neon!
I've got a feeling, just going by your description that you are experiencing an engine misfire, that hasn't tripped a code yet. Very common, and many people describe it as the transmission jerking when pulling hills or at lights..
Let's do a simple test shall we? In a safe area (nothing in front of you) start the car, put it in drive, and while holding your foot firmly on the brake
to keep it from moving, gently give it some gas. See if you get the same feeling your getting while climbing a hill. Don't do it for more than 20 or 30 seconds. I must emphasize to make sure that you have room in front of you in case the car goes ahead on you.
Give it a whirl, and let me know if it feels like what your experiencing when climbing hills. If it does feel like the same thing, the fix is to replace the spark plugs and wires.
I hope this helps, if so please click accept. If you need more information, don't hesitate to ask!