Constantly Hungry, Dark Circles, Broken Vessel Under Eye, Sickness, Dryness, Itchiness. Done CBC. Help?

My 4-year-old is constantly hungry. So much so that she sneaks food and hides the evidence. She also has very dark circles under her eyes and she has what appears to be a broken blood vessel under her eye. Her skin is also very dry and itchy. She has been sick a lot this winter with the flu back in November and pneumonia in February and lots of colds and fever viruses, but she has otherwise been a healthy child. She only eats organic fruits, vegetables, and meat. We do not have too many sweets in the house and we do not drink soda or eat anything artificial. She had a blood test a few weeks back because I was so worried about her constantly getting sick. I honestly feared she might have something more serious. The white count and rest of CBC came back within normal limits. Her thyroid numbers came back "off," though, according to our doctor, who wants to recheck her in another month. I'm at a loss and wondering if someone there can help.