Welcome to TeenHelp.
I would say that yes, in your case shooting rubber bands at your wrist is a form of self-harm, since you're doing it when you feel sad and you're doing it to feel pain. I'm sorry to hear you're struggling to the point where you feel you need to hurt yourself. I want you to know that you are not alone. There are many others who struggle with self-harm and it's not a battle you have to fight by yourself. We are here to support you.
I've generally found that when the urge to self-harm is strong it can help to distract oneself. There are many great ways to find distractions, including the alternatives list located in the sticky section of this forum. Are there activities you enjoy doing that can give your mind a break? Some things that come to mind are reading, writing, movies, shows, puzzles, crafts, dancing, talking with a friend, going outside, gardening, exercise, and volunteering. There are a number of things you can do; it's mostly a matter of finding a few that work best through you. It may take some trial and error to figure out what works but I think you can pull through. You don't have to keep hurting yourself. There are other ways to cope with painful emotions. Hopefully, in time, as you learn how to manage your pain, you can address the issues that are causing you distress. But for now, focus on trying to treat yourself with kindness and compassion. You are a valuable person deserving of love and kindness, and you deserve to be able to show that kindness to yourself. While it's easier said than done, a little kindness goes a long way.
Remember that we are here to support you. If you need anything else feel free to
PM me. My inbox is always open and I am happy to listen.