Transmission Issue - '96 Mustang GT Auto

Let's say I'm going from zero to forty, my RPMs will hit over 3000, but when it shifts, the RPMS will drop down to 2000-ish really hard, making the car jerk. It's not a smooth drop, it's like a split second. Upon acceleration there is also a very rapid knocking sound. There's no lights on my instrument cluster.

This trouble all started after I had my alternator die, then having the car towed a few months back. Ever since then this problem has been getting worse.

Anyone have any ideas what this could be?

Insufficient voltage CAN cause transmission problems. Check that the ground wire on your alternator is tightly connected to start. From there it gets into a pretty wide range of things that could be causing it, unfortunately.