The exact opinion regarding the same can not be given unless and until the wound is seen.
But considering the points narreted by you, you doesnt seem to worry as you have already taken the proper care.
My advice is that look for the symptoms such as fever
& malise, or yellowish or greenish coloured discharge from wound, which in case ouccr would suggest the persistant infection. In that case you need to rush to doctor.
well I would like to suugest you even though you have taken the proper care, adding oral antibiotics
such as cifixime+dicloxacilline two times a day ( or similar ) & anti-inflamatory agent would hasten the recovery. & in place of neosporin
I will sugest you the application of mupirocine which is the better choice.
If you have not immunized to tetanus
it is advisible to get Inj TT im single dose.