I'm not quite sure what you mean by inanimate experiencer but the difference I see with those two words is as such.
Prickle can be used both to describe a sensation and also to describe an object that causes that sensation. E.g. a cactus feels, or is, prickly because it prickles you when you touch it.
Whereas I never hear people say that and object is tingly. You can describe a sensation as tingly but not an object.
Furthermore the idea of something tingling you is an altogether much softer, more gentle sensation than something prickling you. Prickling implies a spike or a sharper sensation whereas tingle is the kind of word you might also use to describe excitement or soft vibrations on the skin.
As we walked into the concert every part of me was tingling with excitement.
This expresses the idea of restless animation flowing through the body.
Prickle can have darker connotations, related to the verb to prick, like when something sharp goes into your arm you can say:
The spine of the rose pricked me
Something that has perhaps a spiky and coarse texture. Think of how English speakers call the Nopal cactus of Mexico the 'Prickly pear'