We're not doctors, and any doctor worth beans won't diagnose anyone over the internet.
That said, you sound troubled at the very least. Lots of teens go through angst, and it's practically a synonym for being a teenager. But many, many teens don't cut themselves or have an eating disorder. Those things are troubling all by themselves.
I am guessing you've read a bunch of stuff online and wonder what is going on if you are unable to tick off every single depression "box" there is.
You don't have to, in order to have a problem.
I realize you don't want to talk to your folks, and I respect that. However, you need to talk to someone, and in person, not online.
Might I suggest asking to see your pediatrician? You have physician/patient privilege (yes, even though you're still a minor). The only things that can breach it are your consent or if the doctor reasonably believes you're going to commit a crime or you're a danger to yourself and/or others. I am not 100% certain how that would go down given that you're self-harming. I believe the benefits are going to outweigh any consequences.
Even if you, personally, feel you've gotten nothing out of it, the doctor will at least have a heads up that something is going on.
If it is absolutely, 100% out for you to see your doctor, then talk to a beloved teacher or another trusted adult. There is no shame or dishonor in reaching out.