In J.K. Rowling's "Harry Potter" series, there isn't any character explicitly depicted as transgender or described as being "born in the wrong body." The narrative of the books focuses on magical adventures, the fight against dark forces, and themes like friendship, courage, and identity within the context of wizarding society. Gender identity, as a modern concept, is not explored in the original seven books.
 

However, after the series concluded, J.K. Rowling has expanded the universe through her website, interviews, and social media, sometimes touching on aspects of character identity that weren't detailed in the books. Notably, she revealed that Albus Dumbledore was gay, which, while not related to transgender issues, indicates her inclination to delve into diverse sexual orientations in her world post-publication. Additionally, in the "Fantastic Beasts" series, she introduced a backstory for Nagini, explaining her as once being a human woman cursed to transform into a snake, which adds a layer of complexity to identity transformation, though not specifically about gender dysphoria.
 

Rowling's comments on transgender topics outside of her Harry Potter work have sparked significant discussion and controversy, particularly around her views on gender and sex. These statements have led to debates regarding how her personal views might or might not align with the world she created. However, within the text of the Harry Potter books themselves, no character is explicitly stated to be transgender or to have issues with gender identity. Therefore, based on the content of the books alone, the answer to whether any characters were born in the wrong body is no. Any discussion of gender identity in this context is speculative or based on Rowling's later clarifications or additions to her universe.