Mr. Silver,
I 2nd Jolt, actually, in that though everyone says 'give it air' wounds heal faster when kept moist and clean. I'd use a very gentle soap and *gently* clean the entire area to get rid of whatever neosporin remains (it has a petroleum base, so will probably 'stick' well) then use mild sea-salt/warm water soaks (1/4 tsp salt to 1c warm water, any stronger will dry the wound too much) followed by a cool water rinse, then use the 1st aid ointment of choice and some gauze.

I had something similar on my knee, deep, deep gouges, pebbles and debris embedded, etc... I used the waterproof bandages (the ones w/ the clear sort of skin around them) and changed them out regularly w/ antiseptic cream... healed quickly but still left a scar...

please keep us updated...
~Aryn