I feel like you should tell your dad. I know you're probably tired of hearing this but really, don't do it. It's not worth it. I know you're in a lot of pain and that's why you should tell your dad about your arm and mental health. I think your dad would care if you'd tell him the truth. Sorry, I'm not really good with trying to comfort people and give serious talk but in short, I think you should tell your dad. If you feel like killing yourself, seek help from relatives and close ones and talk to them (or therapist). Your life is worth a lot and don't ever forget that.