Laser is usually used for the superficial, red portion, while surgery would be needed if it has a deep component. My youngest had/has a hemangioma on the right cheek, just below the eye. She was on oral steroids for 3.5 months, had a steroid injection, then had plastic surgery at 11 months and 2 years, 4 months. She still needs some laser.
If you would like, I could email some photos - don't know if your child's case might be similar. Or maybe I can work on getting my photos small enough to post here, as I see a few cases of hemangiomas under the eye recently.