I think my baby may have eczema because she has red patches of rough skin on her cheeks. What to do?

Find out for sure. You know that commercial that goes, "do you want your doctor doing your job? Then why are you trying to do his?" don't try to diagnose and treat this yourself. Eczema on the face is relatively unusual in babies. It could be seborrheic dermatitis, an allergic reaction, a drug reaction, food allergy, or a host of other things. See your doctor, get a precise diagnosis & treatment.