Neosporin H contains antibiotics and hydrocortisone (a mild steroid). A close prescription substitute is Cortisporin ointment. However, applying steroids near the eyes requires extreme caution due to risks like skin thinning or glaucoma. Since your skin is dry and flaky, you might be experiencing eyelid dermatitis rather than an infection. I recommend using a safe, gentle, preservative-free emollient like Aquaphor healing ointment or a dedicated sensitive-skin eye moisturizer first. Please consult an eye specialist or dermatologist to get a proper diagnosis and a safe prescription alternative.