Dog ingested Neosporin?

A third of a tube of neosporin won't do much to a 70 lb dog. Neosporin is just an antibacterial substance. I don't think there are any harmful drugs in it. Watch out for vomiting and diarrhea or a change in behavior. This change in behavior should not be an effect of your stress. If any of those happen, take him to the vet immediately, but it sounds like your dog will be just fine.