Our daughter also has an eyelid hemangioma but on the outer right eyelid so a little bit different than yours. We did see a dermatologist who counseled us against using oral steroids and to do a steroid injection instead. They also suggested seeing seeing a pediatric opthamologist. We're seeing Dr. Kenneth Wright here in LA who is well-known. He is very familiar with hemangiomas on and around the eye and in fact, just today, there was another family in the waiting room of his office with one similar to what you are describing. You might want to give him a call to see if it might be worth it to come out. Or you could email him. Also, one of the best doctors for hemangioma is Dr. Reinisch here in LA.
We did the steroid injection today(which we hope will work to at least stop or slow down the growth). Dr. Wright performed it. We next plan to have Dr. Reinisch remove her hemangioma in a few months when it hopefully stops growing.
Best of luck.