OMG ouch honey! I doubt the neosporin is irritating you. My honest opinion is Cellulitis. A knick from shaving letting in bacteria from the bath/shower/razor/towel etc... Basically with Cellulitis, its a skin rash that hurts like all hell but its caused by a break in the skin letting in Staphulococcus (Staph) or Stretolycocus (Step). It can be harmful to the body it reached the blood but not fatal unless gone too long without treatment. But trust me as you're in pain now, you'll seek treatment waaaaay before it reaches the blood. See the doctor and ask about Cellulitis.
See a Dr, you could have had a reaction to the neosporin.