The Neosporin will not get rid of or cure the boil since the Neosporin will not penetrate the skin to get to the infection causing the boil.
So Neosporin would be useless on a boil.
The best home remedy for treating a boil is to.
Apply A warm compress to the boil and soak the boil in warm water.
This will decrease the pain and help draw the pus to the surface.
When the boil begins draining, wash the boil with an antibacterial soap until all the pus is gone and clean with rubbing alcohol.