I don't think the vet tech knows what she is talking about. I have worked for vets for 30 plus years and I would not give advice like that without it being seen by the vet. I assume this advice was given over the phone?
That is not a normal reaction to a bug bite. I believe you have something else going on, but then again, I am not the vet either.
Personally, I would want the vet out to do a biopsy, the tissue is trying to die off, that is the little holes and such and it is spreading rapidly according to what you said it started out like. I would not be happy with neosporin trying to fix this.
Oh well, not my horse.