Iguana Girl is a manga by Moto Hagio published in Petit Flower. It was adapted into a television drama in 1996.
It is about a young girl, Rika, whose mother views her as being ugly, and favours her other daughter, Mami. Rika thinks of herself as ugly and as an iguana, but after her mother's death, realises that her mother was also an ugly iguana.
Iguana Girl reflects Hagio's own relationship with her mother, and it took her "years to write this story". Hagio saw an iguana in a documentary on television and identified with it, feeling it was "lamenting its failure to become a human, just like me".
More info