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We say in Japanese something like "I have a cat's tongue"
meaning "I can't eat hot things."
Is there any such figurative expression in English?

Thank you.
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no I don't think so.

We do say 'cat got your tongue?' when someone is not speaking when we think they should!
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Itasan"Cat got your tongue."
That's interesting. Because the cat doesn't talk much?
No, probably because you don't speak, so I assume your tongue is missing, eaten by a cat or whatever/whoever.
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Thank you, Nona.
"Cat got your tongue."
That's interesting. Because the cat doesn't talk much?
 Marius Hancu's reply was promoted to an answer.
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Yes, I live in Atlanta and the phrase 'cat tongue' here means that you can't drink hot beverages too quickly.

I taught ESL in Fukuoka for two years and one day discovered that my students knew what 'cat tongue' was too, small world.