What are possible causes of an itchy nipple, and who can one seek help from?

The description of your rashes seems like hives. That being said, it is safer to consult a doctor to confirm the diagnosis of hives. If it is hives, both classes of oral medications: 1) anti-histamines such as cetirizine, telecast etc and 2) a short course of low dose oral prednisolone (steroid) should be prescribed by your doctor for quick and effective recovery. Topical steroid medications will be ineffective. Calamine lotion can help with relieving itch but it does not help with controlling the underlying inflammatory response.

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.