I think this is I'm being raised by villains.
The protagonist, who is hated by her family (in the real world), wakes up in a novel she really likes. She takes over the role of a girl (with pink hair), but she is an animal person who can turn into a lizard and does so involuntarily when she is very stressed.
The son of a powerful duke, has claimed that she is his child and took her in (that happend before the protagonist woke up in this world). The dukes bloodline is mixed with dragon blood or something like that, there was no distinction into clans.
Later on she meets a boy with purple hair, who she recognizes as one of the protagonists of the novel and helps find his family, form which he is seperated.