Could this be staph infection?

If you had an infection, the area should be getting visibly worse such as more and more redness, red streaks running up the palm, greater pain all the time, increasing drainage. It is important to realize that Staph (better known as Staphylococcus) is a very common bacteria and it basically exists on all of our skins as a common contaminant. The issue regarding the immune system is that in severey compromised people such as those on chemotherapy, those with AIDS, those on systemic steroids have less ability to fight off infection. You having had a short illness a while ago are unlikely to be immune compromised. Stop the Peroxide as this actually slows down healing. Apply the topical antibiotic cream, keep it covered and it should heal shortly unless there is a foreign body at the base in which case, it will need to be removed.