Mysterious cuts on my fingers

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The other day I noticed mysterious cuts on my fingers. One is on the inside of my right thumb, and the other is on the inside of my right index finger. They are deeper than a paper cut. I don't remember cutting my fingers at all though. I thought they started to get better but then they got worse again. Could dry skin do something that drastic? Has anyone else ever had a problem like this? I wrapped them in Band-Aids today, and I'm going to leave them that way until they get better!