I do all my own shots and, touch wood, have never had a major problem. I did have a site reaction to a Strangles shot before there were nasal Strangles vaccines, but that's been the worst of it.
I have given banamine in the neck, back before we knew of the problems, but now I give it IV or oral if the horse is either too dodgy for me to be comfortable going for the vein or if the horse's condition is poor enough that I question whether I would be able to hit the vein. And of course, any time I think I can't accomplish something, I leave it for the vet.
One thing I do that I've not seen a lot of horse people (or livestock people in general) do is, I clean the injection site right down to the skin, every shot, every time. I don't want to push a pathogen IN when I stick them with the needle. So far in almost 50 years of being with horses, I've not had any injection site abcesses, again touch wood.