It would have given her a really good correction! Here's the problem, she took off and you got hurt. She had no correction for it because it was self rewarding. So yes, I think most likely the prong would have helped. Put it back on her and get your clicker back out. And work on proofing the behavior you want (not chasing) by having someone throw balls and taking her places specifically to proof for such things as squirrels and wildlife.
Pretty much prong. No point in getting a clicker back out at this point as the dog knows what to do she just doesnt necessarily care. If she took off shed have hit the end of the leash and the prong would have nailed her good. If you marked with a no and even punished with prong after to nail the point home it would have been ideal.
Never taking your eyes off the dog is not a bad idea either. You missed signs of her loading up for chase.