First, I'm not a doctor. Yes, you really should get medical attention and though you may not want to, you need to discuss how it happened so you can get all the types of treatment you need, physical and psychological. I was in therapy with a psychologist for 6 years and despite how some may make you feel about it, there is no shame in seeking help when help is needed. Hope things get better for you soon.
Hello~We are not doctors here, we are here to help or give advice. I would certainly get some medical attention for this, it is not normal to want to self harm. I am not judging, I am stating a fact. You need psychological therapy, a good one will do you loads of good.
You also need medical attention for the wound you have created and to get that stick out, you certainly do not want to be walking around with a stick in you arm. It will get infected whether you take it out or not, a doctor needs to take care of it.
Please get help.