I drank an ICEE slushie from Burger King and slurped up a human nail can I file Suit?

No, because you need damages to sue and you have none. It is rotten, yes, but the best you can do is complain to the manager to see if you can get a new slushie. The proof however was swallowed so that may be a problem, too.

Check with a lawyer in your locale to discuss more of the details.

Good luck to you.

God bless.

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I cannot improve upon the analysis given by my learned colleague, Mr. Brinkmeier.

Good luck to you.