Can you use a potato to draw out an infection from your finger?

No... A potato is no help for a finger infection. The only situation where a potato might help is for treating a single small pimple near the surface of the skin. Doctors sometimes recommend putting a warm wet towel on such a pimple, to help it go away. Perhaps a warm, baked potato can substitute for the warm wet towel. As for a finger infection, a doctor should check (infection can spread to the hand).