What did I feel testing a car battery?
A multimeter in ampmeter mode is basically a short.

If you're lucky, the multimeter has a fuse that instantly burned when you connected the battery – a charged, a shorted car battery can easily source > 80 A, and that just vaporizes a lot of on-board conductor traces.

So, what you might have been feeling is


the electromotive force due to wires with very high currents running in opposite direction being very close
the thermal reaction of measurement leads most definitely not speced for shorting car batteries (compare your multimeter leads to car jumper wires. Assume that at least 70% of your lead's diameter is isolation.)
something in your multimeter violently exploding and that mechanical shock being sent down the wires.
your nervous system's shock response to seeing sparks and hearing something pop.
Back-EMF: a fuse blowing has very high derivative of current over time, which means that the very little inductance of your wires might have caused a very high voltage for very shortly, think a couple kV. That might actually have shot through your isolation, but honestly, the resulting current would most likely have been low enough to not pose a danger