I'm not sure but my guess would be hemangioma from what you've described and from the picture. I would continue to take pictures every few days to show the growth/progression of it. It's a little harder to see the birthmark on her eyelid so I'm not sure about that. I think it's a good idea to be seen by a vascular birthmark specialist and they could tell you more definitely and also discuss treatment options, especially when the eye is concerned. It is also possible that it will fade on its own but at least you will have someone monitoring it and you will know what your options are if you choose to treat it.
VBF Hemangioma Forum Moderator