M.B.
Getting attention is a great thing for any kid, no matter the mechanism or path used to get it. Your daughter only knows that when she has a tantrum or self injures, she is getting your attention. The likelihood that this is something else has got to be small, but can't be ignored.
Try this. When she starts throwing a fit, walk away. Don't turn around, don't look, don't talk with her. If she comes running to you and brings her fit with you, tell her nicely and calmly (yeah, right, easier said than done, but try) that you can't hear her because she is too loud, and walk away again. I have done this in HEB, WalMart, Costco, the park, etc...but only when I know the environment is safe, and no one can grab my children etc. If this works, and it probably will just because of the shock to their egos that their fit is not involving the world, use the technique as long as you can. I still use it on my 9 yr old when I have to. (not that his fits are so public anymore...).
But, if your daughter continues to hit herself...well, tell her if she wants to hit something, she can it a pillow, get her a special pillow for that..may be a black square pillow or something that can be labled: Hitting Pillow...and let her go at the pillow. Encourage her to hit the pillow at the first sign of frustration that is overwhelming to her. And tell her when she is calm and can talk to you, you are there to listen to her.
If she continues to hit herself and or hurt herself, talk to your doctor, and a professional if need be. You don't need to have her learn that injuring herself gets attention or is a stress relief. That, as you can imagine, leads to big big problems as a teenager!
Good luck, and our thanks to you and your husband and family for his service. God bless!