Should I see my doctor about this?
Yes. Even if you don't think you need medical attention on your injuries, self harm is a sign that there is something wrong in your life, or unhelpful about your coping skills or other. If you see a doctor, you can discuss these things and hopefully get you the help & support you need to work through it.
This might include a counsellor or psychologist. Helpful information about seeing doctors can be found in
Seeking Professional Help.