It doesn't seem like a wart, because it's under the skin. I can see a layer of skin over the white bump. I was thinking it is some type of fungus, but I can't find anything on the internet that resembles it.
Hello,
I cannot confirm anything without examination but it can be keratosis punctata(benign, largely asymptomatic condition of the hands which presents as a wart), callus, verruca or keratoderma. Place protective covering or bandages over the sore to decrease friction on the skin until the sore heals. Soak hands in warm soapy water to soften calluses. Then rub with a pumice stone and apply some moisturizer. If the symptoms persist then please get it examined from a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.