Please get help! This is not the kind of thing you should be going through alone. It only makes you feel more guilty and ashamed of things that are not your fault!
You cannot control, nor are you supposed to be responsible for your father’s behavior. The only one you are responsible for is yourself, and this includes your health. Cutting may feel good temporarily, but the scars remain forever. The best thing you can do is find someone healthy you can talk freely with, whether it’s an anonymous hotline, or a school therapist. These people are here for people like you (and me. and everyone who suffers silently while pretending everything is normal)so you can talk and see that you’re not alone, and there are ways to help you.
Also understand that when you’re personally involved in a situation, not to take a speech aimed at the general public as applicable to all situations. I do not know the speech, nor am I sure of what Rabbi Wallerstein was referring to, but I know he would never blame your father’s addiction on you. If his speech really affected you, perhaps it would best to speak to him for clarification with specific details of your situation.