So apparently I'm a woman beater?

I'm a 16 year old male, and according to my family I'm a future woman beater.
I have punched my mom once and my sister a few times.
But the thing is, I didn't hit them without a reason.

During my childhood if I did something bad (got home too late or used like 5 dollars too much on candy) my mom would hit me for it. And no, it wasn't a slap. She used a fly swatter or some other kind of tool to hit me with (usually ended up with a welt or something). At the age of 11-12 I had enough and punched her. Since then she has stopped hitting me.

And now comes my sister.
When we have arguments I am able to keep my cool, but the thing is she gets extremely angry. And when she gets angry she scratches me with her nails which causes me scrathes that bleed.
I have multiple scars from them.
One day we had an argument and she decides to break my 100$ headphones which I payed for myself. I got angry and basically punched her once.
After that my other sister smacks me in the head with a plastic board which breaks in half.

All kinds of things have been happening between me and my family. I am not sure have I just been bottling up too much anger.
When I hit them it just happens. I can't control it. (I have never hit anyone else except one bully and my mom/sister)

I regret what I have done to them but they keep mentioning those things when we have an argument and sadly that opens up the old wounds.

I believe I am angry but I just don't know it (this makes me act like a douche if I hate someone).
My oldest sister used to boss me around and if I didn't listen she would slap me.

I treat most people nicely. I have a girlfriend but I would never hit her. All these things I did years ago but they keep mentioning it which makes me really sad.

I want to be a doctor to help people, but I just can't see my future as a doctor. My family always say I'm not good enough to be a doctor, or that I am too angry.
I am angry at them.
I'm the type of guy you can trust to help you.
Updates
+1 y
I would never hit a woman. But the thing is I did this years ago. When I was going through early stages of puberty and I wasn't really emotionally stable. Please read the whole story before judging... I just came to ask for help. I know I shouldn't hit women. I don't really know what is right or wrong anymore...
Updates
+1 y
If my past cannot be forgiven and I'm still seen as a monster then I see no purpose in this world for myself...

I did this many years ago, I have been trying to get help. But they still keep cursing at me and telling how worthless I am for my past doings...

I can't even ask for advice on here...
So apparently I'm a woman beater?
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