If a cat gets sprayed by a skunk and then tries to clean himself, can the cat get sick?

My cat got sprayed a few days ago by a skunk and we've tried everything. When the tomatoe juice bath didn't work, the lady at PetCo suggested to give him a bath in vinegar/water douche. That worked a little better. He still smells a little funky, but we are more worried that he's sick now from trying to... show more My cat got sprayed a few days ago by a skunk and we've tried everything. When the tomatoe juice bath didn't work, the lady at PetCo suggested to give him a bath in vinegar/water douche. That worked a little better. He still smells a little funky, but we are more worried that he's sick now from trying to clean himself. So, what I'm trying to figure out is: can the skunk spray make a cat sick?
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