Rashes actually develop from antibiotic use (among other reasons). Antibiotics destroy the good bacteria in a child's colon. Your daughter is in need of this bacteria being replaced, which will eliminate both the rash and the regular ear infections.
Acidophilus (found in yoghurt as well) is good bacteria available almost everywhere in chewable form for children. If you can't find it chewable, buy it in the powdered form and put 1/4 teaspoon in her bottle or milk ~ it is tasteless.
If you decide to give her yoghurt instead (which will also work but may take longer), make sure it is whole milk, plain and unsweetened. Don't worry about the flavor ~ kids like it, especially if you mix it with bananas or berries.
Google on Antiobiotics and Acidophilus to see what comes up there. You could easily get your daughter off of the cycle of ear infections by focusing on this issue for her.