My daughter is 15mo and she also has eczema. She will scratch her leg folds, eyes and behind her ears. She gets more itchy at night and scratches her eyes and ears a lot when she is tired. She scratches her eyes until they are red and ears and thighs even when they are sore and bleeding. Nightly baths help us and, surprisingly, we recently found that neosporin significantly speeds up healing time, reduces redness and soothes her skin enough to reduce the itching. We also have to trim her nails very frequently!! I think that, when the baby is in emotional discomfort, it amplifies physical discomfort as well, so they will get more itchy and scratch more.
My now 13 year old did the same. She had severe eczema. If you are already treating the eczema and allergies, then she will grow out of it. Unfortunately, due to my situation at the time, my daughter only started to get better when she was almost 2 years old.