Would a shark whip into a frenzy from smelling its own blood?
I'm pretty sure, they can smell their own blood, but they do not attack themselves. Wounding a fish results in the release of chemicals into the water. This is a signal for other fish about potential danger and they will escape (Schreckstoff). Of course, the predator of the wounded fish will not mind. So this seems to work best within the same species. Fishermen and military have apparently used dead or rotten sharks in the past to keep sharks from attacking (Shark repellent). I guess, a similar mechanism plays a role here. Sensing a wounded member of the same or close species (including oneself), would block any feeding behavior.

The Myth Busters have actually done this (not very scientific) experiment: https://youtu.be/E1GenfKR9pk