Hi there. Your daughter is so cute!!! My daughter, who is 5 now, has an upper lip hemangioma with some of it going up towards her nose. I would definitely get a second opinion. My daughter was on oral steroids from 10 weeks-10 months of age. I know that some kids experience bad side effects from steroids, but my daughter actually did very well. She finished the steroids right before she turned one and we have been watching it involute on its own since then. Her doctor has said all along that she would probably have surgery when she was about 5. We were scheduled in Feb. but it got cancelled because she got a cold...and then the same thing happened in March (but that's a whole other story!) I have heard that lip hemangiomas sometimes leave the fatty tissue or extra skin and need some help to look normal.
She has seen a vascular anomaly specialist in Boston since she was very little so I would suggest seeing someone who really specializes in hemangiomas, etc. Or you could email one of the doctors on this website with a photo and they will email you back their ideas. I have found this very helpful. If you would like, email me firstname.lastname@example.org
and I will send you a link to some pictures of my daughter. Hers looks a bit different from your daughter's but the experience has been similar and you get an idea of how hers has progressed over time.