Clean the area with soap and water well, don't put anything over it like neosporin or clean it with anything wierd. Neosporin is generally not used in puncture wound as it is petroleum based abd cab create a nice breeding ground for some bacteria it doesn't cover as the wound can seal quickly over it. Hold pressure to the area, and I mean pretty hard, don't just place a cloth over it with tape. Pressure dressings aren't generally a good idea on the neck for obvious reasons. If it doesn't stop with direct pressure after about 20 minutes you should go to the vet, or if the bleeding is pulsatile which it does not sound like it is. Cold actually makes you coagulopathic and you will bleed more, it has been used historically acutely to try to vasoconstrict, but the coagulopathy outweighs any benefit from minor vasoconstriction so I would not do that (it's actually a JAHCO thing now that patients in the OR have to be kept a certain temperature so this doesn't happen when they get too cold, it's that big of a problem). Remember the old surgical law.....All bleeding will stop eventually ;) The longer you wait to sew things up the more likely it will get infected so keep that in mind.
Here I am stuck in the middle with you
I practice societal sanctioned assault