[~Misguided Ghosts~]

I think that yes, this would be self harm. Self harm can be described as anything that you do to yourself to inflict pain as a way of coping or handling what is going on around you. Since you are punching yourself, even without leaving bruises, you are using a means of physical pain to cope with what is going on, so it would be self harm.

This is a link to a list of alternatives to self harm, which are healthier, safer ways to cope with what is going on. I'd recommend trying some of these out, they're better.