The rules of capital punishment for kids ie spanking, have changed dramatically since I was a kid. Back then, it wasn't seen as child abuse providing the infraction was dangerous to the child, like running out into the road, and that the parent had control of themselves when they did it.
If your son was physically threatening and you were in control, I wouldn't get too excited. Its the lack of control and later injury to yourself that would concern me. Some of the worst self injuries occur when the person is either extremely angry or feeling trapped.
I do think you would be better off with therapy, though I don't know if they would take you as an inpatient for the incident. Once we become mothers or fathers, we have a responsibility to save them from having to be our caretakers or witnessing a SI or suicide attempt. The fact that a simple argument ended in SI, I think you realize there is a problem. You wouldn't be here if you didn't.
If you want a cold shock of reality, there are a couple of web sites with photos of what people have done to themselves. Its more than just shocking. I was a deep cutter into muscle, but the photos shocked me. Most of those people probably started with shallow cuts or hits or burns.
You may not like this answer, but before you dismiss it, think of how it looks to your son. You don't say how old he is, but you can bet that if you have SI'd before, he lives in fear of it happening again. People argue, but that doesn't mean they don't love each other. Make some calls and get yourself into therapy. The alternative is not what you want.
Sam2