I very much wish I had specific answers for you, but a lot of what you are worried about and asking about depends on your specific location. I'm absolutely not asking for that information and please do not post it for your safety, but it might be a good idea to look into the specific laws for where you live.
If you are based in the US, each state will have different laws regarding this. I live in Michigan, for example, and here, someone who is 14 can receive 12 sessions or 4 months of outpatient therapy without parental knowledge or consent, but if further treatment is needed, or anything beyond outpatient therapy is needed (eg meds, inpatient, day program), parents or guardians would need to be informed and consent to that. Here, they will not notify parents (within that stated time frame) of the child even being IN therapy unless there is a 'substantial risk of harm' to the child. Where you might run into trouble, if you lived here, is that they do not define what a 'substantial risk of harm' is, and different providers often have different ideas. To some, only suicidal intent indicates substantial risk of harm. To others, self harm might fit that.
I think that in many circumstances it is absolutely more effective to gain parental consent for mental health treatment as you will be able to access more complete services, but a lot of states in the US do have provisions where minors can access some mental health treatment without parental consent. I would really urge you to perhaps speak to a teacher or counselor or other trusted adult (I'm aware it's likely summer break) who can help advocate for you with your parents if they aren't taking you seriously. You really will be able to access more complete care that way in most places. I would also suggest, if and when you do meet with a therapist, you straight up ask them about what their policies are and what they would need to inform your parents about. In many areas there is some level of professional discretion at play, so while I do think there is some likelihood that providers may feel a need to inform your parents, I had pretty varied experiences with that from different providers when I was younger.
My parents were informed when I disclosed my self harm, however it was at the same time as disclosing suicidal thoughts so I'm not sure how it would have played out had that not been a factor. I had some therapists who disclosed every incident of self harm, but I had others who didn't disclose really much at all, and gave me a lot of autonomy as long as I wasn't a risk to myself in terms of severity. So your mileage may vary, but I would absolutely ask policies from the start.
So basically, tl;dr is: it varies, and even in places where you can access care without parental consent, there's often benefit in having consent, so consider getting some help to advocate with your parents, and different therapists do tend to have somewhat different policies on how they handle self harm, so totally ask about their specific ones.