I don't see anything "wrong" or disturbing about the frequency of your masturbation or the cuckold fetish that arouses you.

When I was your age, I'd masturbate daily or every other day. Sometimes twice a day, but rarely did I need or want it more frequently than that. So I'm not seeing that this is an addiction. And anyway, addiction isn't just about frequency. Rather, it would be if you use it to escape real life, especially if it interferes with your job or operating a motor vehicle, for example. And you're not engaging minors online or "crushing," both of which have an immoral leaning. A professional might disagree and say that your behavior prevents or delays real intimacy; I doubt it, though.

Also when I was young, I felt ashamed and wanted to limit or stop. I was raised Catholic and actually "confessed" about this behavior a few times. If there was any harm, it was that I had developed a distorted sense of females as sexual objects, even without looking at porn.

You are correct that "something will leak out" unless you pay cash. Insurance coverage provided by a parent would generate an Explanation of Benefits for every office visit. At the very least, the information your parents get would include your name and the practice name and (I think, maybe) codes for diagnosis and/or procedure. These codes might be very general though; it would be hard to infer the specific issue or treatment (if one is offered.)

I am very impressed with the courage it took for you to reach out and write about your issue. Even though this is anonymous, the disclosure still took guts.