It was a good idea to reach out and talk about what you have been going through. If you don't feel like you can talk with your school counselor but feel you need the help, why wouldn't your parents be an option for you? They would be the ones that could get you the help that you are looking for.
Hitting yourself to cope with whatever you are going through is unhealthy. If you are dealing with anger on a regular basis, it is important that you talk with someone. You deserve to talk with someone to help you figure out what you are going through and to help you find a better, healthier alternative.
Here's an idea that may help. If you want to start out with talking with your school counselor before talking with your parents but are afraid, like you mentioned, that they will tell your parents, try this. When you go to talk with them, let them know that you are nervous about talking with them because you are afraid they will tell your parents. Tell them that you are looking for some advice on how to handle anger and then go from there. Be honest with them about hitting yourself so they know exactly what is going on. The more they know, the more they will understand. If they know you are nervous they may handle things differently.
Anger is tough because we hold onto it so many times. Dealing with it in the right way may take some time and some direction from the counselor or another adult. If you don't journal yet, give it a try. Get a notebook and start writing in it about how you are feeling. Don't worry about neatness, spelling or anything because this is just for your eyes. This is your way to gain control of what is going on. You can write letters and not send them to people, write feelings and why they are that way or you could draw or write poetry. Whatever you feel you need to do. If you have a hard time getting started, check this out.