I know what it is like to have all that rage inside. There was no way to let it out, and at night, I always lay in bed thinking of some brutal wars I fought in. Or I would just punch the wall to bruise my knuckles.
But I found out that there are ways to get the emotion out, a lot of ways. You could write things down, about what is bothering you. Just shut down your mind and start writing whatever you feel like writing. After that, you could read your story, and think about what exactly is bothering, and what are possible causes for all that emotion. I found out that I needed someone who care'd for me, but due to the mask I put on, no one ever saw that I needed help. And I didn't want to start about it, because of the fear of being rejected, bothering people etc. They had to come to me while there was no way they could know.
Another way to let the anger out is physical exercise, though I do not know whether this is good. When I felt hopeless and angry, I would do physical exercise, or more like physical torture. I would go running or rowing until I literally fell down. Then I would stand up and continue until all the anger was gone. I don't know whether this is good for you, but it did made me feel better, and I never discovered any physical pains or problems with doing this.
You can also turn to write down your thoughts in poems, and even better (for me :) ), music. Whenever I feel something coming up, I start to improvise on the piano to get my thoughts and emotions out. This works amazing, I become relaxed, in peace again. Maybe that there is something creative that will work for you too.
But the most important factor of your rage can be the hormones. I think you are still a relatively young person (as I am), and well, hormones are a part of that. And of course, the older, the wiser :). The older you grow, the more insight in yourself you will get, in how to get rid of the excess of pain and locked up emotions. For me, it was music and meditation to get me in peace again. If I feel something coming up now with no piano around, I'll just try to stay aware of the feeling inside my chest, and accept it for what it is. As long as I am aware, the feeling can't take over, and so there is no problem.
I hope you will find your way of dealing with it, and just remember it is not uncommon for people to have these emotions. And I suggest that either you yourself or with the help of a professional will try to find out the reason. For instance, do you feel the hatred when being alone on a sunny day in nature, listening to the birds? Do you feel hate against nature, or only humans? Are there people to whom you will never, or always, feel hatred? Questions like that.
All the best, and remember writing is good way for letting the emotions out, and you can always tell me if you want someone to listen!
Acceptance is the key
Existential depression and Insecurity
Try to keep smiling! :)