Hi N., unless you put ponytails all over her head, you are going to have to break down and apply some cream, oil, gel what ever you decide. I am a licensed cosmotologist as a hobbie and help run my husband cable mfg business during the days. My suggestion to you is only put a little hair product on her hair, you would be amazed that a little of oil or gel goes a long way. Yes if you use to much it will become greasy, even try a little baby oil. My hair has the same issues out here especially when it is humid, frizzzzzz, frizzzz, frizzzz. Stop at any beauty supply shop, most of them serve the ethnic type of hair. Don't worry you will find something. Remember just a little dab will do you.
Take care of that little beauty you have, when she becomes older there are permanent formulas the will calm, relax, or completely straighten her hair if that is what you wish.