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This is called NIPPLE DERMATITIS
...a kind of allergic reaction
of nipples...apply a moisturizer cream along with a mild steroid cream like hydrocortisone cream
....also take an anti allergic medicine like cetrizine (10mg) daily for 7 days...If cuts are deep then also take any antibiotic tablet like azithromycin(500mg) daily for 3 days...It would be good to consult a dermatologist
for above prescription.