M.R.
My son just had that problem. His finger started out a little red and a bit swollen, then a week later, it was hard skin. I trimmed it off and his finger, right by the nail, was really red and swollen. I went to his pediatrician and she said it was a deep tissue staph infection. She was concerned because it was close to the bone. He went on oral antibiotics (I tried to avoid these, but because it was so close to the bone and deep tissue, she said it had to be). He was also perscribed a topical antibiotic and soaking his hand in a solution to dry it out. So, go to the doctor ASAP.