Rice Cereal Allergy?

My Daughter is 4 months 1 week, and the pediatrician has told us to start rice cereal. She has been getting rice cereal in her bottle to help withrwflux since she was 2months  old. She has had Rice cereal spoon fed to her about 5 times and loves it. But if she gets it on her face she breaks out into a little rash. Not sure if it's just contact dermatitis or maybe she's allergic to it. Anyone else's baby have sensitive skin with rice cereal?