You know, I think this is an important question, and it really hinges on your definition of self-harm. "Self-harm" sort of gets wrapped up together as if it was all one thing but, of course, it's really not. There are all sorts of things that people do to their bodies that cause pain and damage. Some of those things are socially sanctioned and some aren't, and some are more unhealthy than others. Some people who get tattoos and piercings do it because they like the pain, and wearing high heels is far more harmful to the body than superficial cutting. Some people who smoke really do use it as a kind of slow suicide. Men who punch walls in anger sometimes end up breaking their hand so badly they need surgery.
The way I see it, all of these things are self-harm, but some of them aren't usually thought of that way. In my experience, harmful actions which conform with gender roles or are male-associated are not usually considered a form of self-harm, while actions that transgress gender roles or are more female-associated are more likely to be considered self-harming. A man punching a wall, a woman getting a piercing is not self-harm. A teenage girl cutting, or a man getting body piercing often is. I find the concept of self-harm much less useful than trying to break down the components. I ask myself: why am I doing this? Are the consequences of this action acceptable to me? If not, what else could I do instead to meet the same need?
So, try asking yourself why you actually bind? Is it because you don't want other people to see your chest, or because you don't want to see it yourself (social dysphoria or body dysphoria)? Or do you actively want to hurt your chest, and bind it as a sort of self-directed revenge? When you leave your binder on even if it's hurting, is it just because the pain of leaving it on is less than the pain of having to deal with your body when you take it off? Or is it because you want the pain-- want to feel it, or think you deserve it? It might be several or all of those reasons at times. But breaking it down is likely to get more answers than just asking if it is "self-harm."
Binding is harmful-- but for lots of us it does more good than harm.