No, no-one gets human TB from fish. However, there is a disease refered to commonly as "fish TB" which is (the only?) known zoonoses bacteria between fish/humans, and this can enter broken skin and cause a granuloma-type infection.
It isn't TB as in BCG / coughing up bits of lung for months on end /etc, it's a skin infection. Hence the TB vaccine (a vaccine against TB, known as the BCG) wouldn't have any effect on it. Is a different ailment.
It's also pretty rare and even if your fish did have it, you would not be that likely to catch it anyhow.