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There's a bit of miscommunication here.

Nothing travels faster than c, or the speed of light within a vacuum.

The speed of light within a medium (like water) is not c. It is less.

When a particle is traveling at c and slams into a medium like water with enough force it will continue traveling faster than light normally would in that medium, and give off that radiation as it does.

But it is not traveling faster than light as you emphasized. It is traveling at nearly c and getting slowed down. It is often referred to a "light based sonic boom" though because that makes sense. But only when you consider the transition from vacuum to a medium or medium to medium.

Protip: anytime someone points out a thing is traveling faster than light they're wrong because really: nothing does ever. It isn't physically possible and the smartest minds on the planet have tried to reason how it might be for nearly a century now, with no progress at all. There are workarounds but they don't involve "travel" in the real sense, more like displacement.