Do you guys have an antibiotic cream called Furacin? That's what we use instead of polysporin/neosporin. We get it at Greenhawk or from our vet. It is a great product becasue it helps healing from the inside (according to our vet). I've dealt with a lot of dog bites (I have 20 sled dogs). They are very dirty and full of bacteria. We almost always put the victim on antibiotics. If you can't do the antibiotics, I would clean four times/day with bedadine solution. Slather the wound with Furacin and wrap with gauze and vet wrap. Spray the bandage with Blukote to keep the flies away. I would do that for the first 3-4 days. Then if there is no sign of infection, I would switch to 2X a day cleaning and blukote no wrap. Unless really bad, we don't use stitches on dog bites because it traps all the bacteria and infects much easier.
Logic says to dry the wound as fast as possible but with dog bites 'cause they are so dirty they should be kept moist for a few days so the bad stuff can drain. If you dry it out too soon all that bacteria is being trapped inside. (This refers to a wound that is severe enough to require stitches). I am far from being a vet this is just what seems to work for us.
Good luck with everything. I lost two baby goats to one of my dogs two years ago. It is a horrible things to have to go through. I feel terrible for you and I'll be thinking of you today.