My daughter keeps getting sores in her scalp that are open, then scab over, then flake off of her scalp.?

First it was right in her crown and I brushed it off as she has a dry scalp and she likely scratched her head too much. Tonight I found two more areas in her scalp that are scabbing over and have a couple of open sores. (not big, but open none-the-less) The area that healed was almost peeling off as a sunburn would. We had battled lice for a couple of months because someone at her school had it and wasn't getting treated and she kept getting it. (I would catch it really quickly because after the first time I started checking her regularly so most times there'd just be one or a few in her hair) I started using olive & tea tree oil in her hair to deter lice from wanting to get in her hair. Which has helped, but now we're battling scabs and large flakes. Could there be a connection to the lice she was getting and these scabbed areas? (after the second round of lice I stopped using the pesticide b/c she's so young, I was using natural methods to rid her of the nits) I also have trouble getting her to eat enough food. She'll eat very little then say she's full so could it possibly be that she isn't getting enough vitamins?