I can really relate to the feeling of not being satisfied and wanting to keep going. But please try and take care of the wound!
Totally understand not wanting to tell your parents. I've been cutting since 15 and have never told my mum. If the wound gets worse though, you definitely need to let someone know. You don't want to risk it getting infected.
I agree therapists are not very helpful when it comes to self harming, but they could help you understand the urges.
Honestly therapy is always worth a shot; especially if you're in the UK and can get it for free. Depending on your age, your parents don't even have to know about it, which I think makes you feel less pressured.

I'm here if you ever need a chat! Best wishes