What is wrong with my 03 Dodge Neon?

I bought this car about 2-3 years ago and it currently has 142700 miles on it. A few months after I got it, I noticed it would occasionally lurch when I accelerated, but it wasn't happening often enough for me to really worry about it. Over the past month the problem has gotten significantly worse to where my car will lurch when I'm going from a stop to accelerating, accelerating while already going, or even slowing down at times. I have also noticed that my speedometer is flipping out-sometimes I will be at a dead stop (0) and accelerate and the speedometer won't move when I'm obviously going. After a few seconds it will shoot up to 40-50 when I'm only going at max 15-20 mph. At times the lurching and speedometer problems happen at the same time, and other times separately so I'm not sure if they are related or not. We have guessed that it is maybe a speed sensor but I'm hoping there is someone out there whose passion is cars and can either confirm or correct this guess. Any and all advice would be greatly appreciated. Thanks in advance, guys!