A wart on my finger became infected & I treated it with neosporin for 2 days. Swelling went down, Now it turned brown? Safe to peel off? Is it dead?

Hyperkeratosis. The wart virus causes the development of thickened skin like a callous. The treatment is to remove the dead skin by paring it down. Can be done at home with care not to cut too deeply into the skin (and not cause bleeding)