When a baby is teething the teething does not cause Eczema in babies.
However the teething can cause the Eczema to get worse.
The baby with Eczema already has skin that is easily irritated so when they're teething it makes the Eczema worse.
Most times babies will stop getting Eczema by the time they're ready for kindergarten and it usually goes away on it's own.
If your baby has Eczema you should bathe your baby everyday and apply some moisturizer to the babies skin to keep it from drying out.