Hi,
This could be a part of Cheilitis, which is a medical condition involving inflammation of
the lip. Or a bad case of Chapped lips , a condition whereby
the lips become dry and possibly cracked. It may be caused by the evaporation of moisture.
Whether this is eczema or not cannot be said with surety without having a look at the lesions.
Lip balm can often provide temporary relief, though it should not be used extensively.