Food Allergies Treatment

Is she allergic or just lactose intolerant? Those are two different things. Allergy is usually toward the protein in cow’s milk which is the same in organic milk and in regular milk. Organic milk is better in the sense that it comes from animal that have been raised in conditions with much less chemicals and hormones as close to nature as possible than the milk that comes from regualr farms and which may contain some chemicals or hormones that my provoke intolerance in a baby. Children usually outgrow food allergies but before you try, you should consult your pediatrician. S/he might recommend to try or not to try depending on how bad the first response to milk was.
Then milk intolerance is a different thing. It is the inability of the intestines of digest the lactose in the milk (this is a kind of sugar, not a protein) and the result is persistent diarreah. That condition, although troublesome (I am milk-intolerant), is not dangerous or life-threatening so you can try giving milk and see how it goes.

It makes no difference if it is organic or not. Your baby will still be allergic. You may want to speak to a doctor or pediatrician for alternatives.