If it's on the side of her face that rubs against fabric, then it could be a possibility. My daughter didn't develop eczema until she was 3 mos old. Hers was behind the knees, on the inside of the elbows, & various other patches. We had been using Dreft, thinking that since it was made for baby, that it couldn't possibly be irritating it. But her pediatrician suggested using All Free Clear, as well as switching to an unscented baby wash, such as Eucerin Aquaphor Baby Wash, or Cetaphil. We tried many kinds of free & clear detergents from Tide to Purex & everything in between & All was the only one that doesn't irritate her. We also had to use the parfume free baby wash & if we use a scented shampoo for her, then her hair must be washed & rinsed clean before filling the tub for her bath. We also haven't been able to use the so called eczema creams, since everything burns when she has a flare up. The only thing that she can tolorate is A&D ointment. Can be a little messy, but it's the only thing that works for her. We also wash all new clothes before she wears them.
She just turned 4, so we have been dealing with it for years. But overall, all of the changes that we have made, has been a huge help. Now she only seems to have flare ups on occassion in the cooler months when she has more fabric covering her flare up areas. Or when she goes to stay with her grandparents, because they never listen to what I say : /
You should still talk to the pediatricain about it, just in case it's something else, but if it is eczema, I hope this helps! :)