I agree that an AntiB injection is warranted here. I would have phoned my vet to ask which one would be most appropriate. A deep penetrating wound is dangerous - trouble might not become evident for quite a while. The advice not to use AntiBs unneccessarily applies to actions such as routinely giving watery mouth mix to all newborn lambs whether they need it or not - and for most of us, especially if we lamb outdoors, it's not.
The problem which arises from overuse of AntiBs is resistance - if animals build up resistance to the drug, or the particular bugs build up resistance to the AntiBs, then there would be nothing left which would be active when we have a genuine need for them, as in this case. Also there is a difference between giving AntiBs to breeding stock and to meat animals, from the human consumption viewpoint, which might make you think twice, but still the animals welfare has to come first. Nowadays we all have a duty of care towards all our livestock and this little animal should get its shot.