Probably, but. I would not blow it off. Many infants are allergic to a food that is causing the rash. Getting an allergy evaluation to determine if a food is related to the rash may help to dramatically improve the rash once the food culprit is eliminated from the diet.
It could be. Eczema on the arms and legs is more likely to be on the inside of the elbows and the back of the knees. The face is a common site for eczema in infants.