Sorry to hear you are having a flare of your eczema in addition to trying to look after a young baby. I would advise that you see a doctor or dermatologist so that your condition can be looked at and treated quickly.
If there is weeping from the breast, the eczema areas may be infected. Usually topical antibiotics and steroids will help treat your eczema quickly.
If the condition is quite severe, sometimes oral medicines may be added. Eczema is easily treatable so do approach an experienced doctor for help. This will allow you to breastfeed your child comfortably again. Hope you feel better soon!
Warm regards
Dr Stephanie Ho, Dermatologist