Yes, your health should come first and taking care of yourself would be the best way to be a good role model for your little brother. Wouldn’t you rather teach him to deal with his problems directly rather than deny them?
I am not sure why you get so angry with your mother either, but I do think it is worthy of looking into it with the help of a trained professional. Hurting yourself in order to deal with these feelings suggests that you could benefit from improved coping skills. Learning to better understand your feelings and developing a variety of problem solving techniques will not only help you now but for years to come. Perhaps a therapist can also help you understand why you have such extreme feelings about your mother.
Lastly, if you are concerned about what your family would think of you seeking help, why do they need to know? Therapy is confidential. No one needs to know that you are going or what you are going for. If for some reason it takes a while to find a mental health counselor, I would suggest that you get a book or workbook on anger management so that you can immediately address your issues.
All the best,
Dr. Holly Counts