No, I don't consider skin picking to be self-harm, at least for those reasons. When I was in fifth grade I had an awful habit of picking at my skin to the point my parents made me go to school in bandages. Yet I don't consider it self-harm because I wasn't doing it to hurt myself in some way, it was just compulsive. I don't know if your skin picking is compulsive or not but it doesn't sound like you're intending to harm yourself while you're doing it; ergo, I wouldn't call it self-harm.

And congratulations on almost three years self-harm free! That's a huge accomplishment! Way to go.