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11 day old - skin around finger

Hello, my little one is 11 days old and I am worried about the little bits of skin around her fingers. There is a bit around her thumb that looks to be a little sore and infected. I have added some pictures below.. (sorry for the poor quality) Can anyone offer any advice? I put a little bit of antiseptic sudocrem on it. Any reply would be appreciated - I am a worrier!