Either is correct in this case. According to MW, we can define "dislocate" as:
to move (a bone) out of its normal location or position in a joint
Since the piss shivers are causing you to jerk your jaw out of place, both you and the shivers can be considered the actor here, and you can say that either one almost dislocated your jaw.
The last sentence ("got dislocated"), while not the most common phrasing, is also correct. "I had piss shivers so hard that I almost suffered a dislocated jaw," is another good phrasing.
But let's answer the deeper philosophical question behind your asking about the piss shivers. Can you say "I dislocated" something if you didn't do anything? I would say yes, in most cases. If a friend of mine (call him Steve) were tackled randomly or struck suddenly by a car and suffered a dislocated joint because of it, it would not be bizarre for me to say "Steve dislocated his pelvis when that guy tackled him" or "Steve dislocated his elbow in the wreck". The only scenario I can conjure in which it seems inappropriate to say that Steve dislocated something is if someone (not Steve) is deliberately, carefully popping Steve's joint out of place.
All in all, if there's even a small element of chance in whether or not something will lead to a dislocation, you can say "I dislocated". However, if you're unsure, making something else the actor is perfectly fine, and we can say that "the wreck dislocated Steve's elbow" or "that guy dislocated Steve's pelvis when he tackled him".