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Usually, a lump that is cancerous would not be sore or painful. These are usually painless. Most likely you have a small cyst under the nipple, which will resolve itself in time. However, it is always best to have these type of lumps checked by your doctor. Sometimes, lumps do not fall in the "usually" category. And since you have had this soreness for about a month, it would be best to have it checked.
As for the white spots on your fingernails: these are caused by an injury to the nail bed. The spots on the nail are like bruises on your skin. But with nails, it takes longer for the spots to show up after the injury, by which time you have forgotten how you injured the nail. The spots will grow out with the nail.