I saw this tip in Jenna Jameson's autobiography.
IMO, I think an anti-inflammatory, like Hydrocortisone ointment works better, but after the shave. JMO.
Neosporin is an combination of several topical antibiotics, it kills certain bacteria on the surface, but hydrocortisone reduces inflammation. However, hydrocortisone should not be used in large quantities. I use just enough to put a paper thin layer over the area shaved and then cover that with B&BW Body Butter.
Also, using too much Neosporin or Polysporin could cause antibiotic resistance, so it probably isn't the best thing to use a lot of, like you would soap or shaving cream. It could also predispose your body to yeast infections, if used in large quantities. Remember that it IS a bunch of antibiotics in a Vaseline-like base.