How do I move to the UK at 16 years old?

I am from New Zealand so I’m not sure if I can post this here but I’m not sure where else to look for help??
For a while now, I’ve urgently wanted to move. I’d like to not specify exactly why though!!! The first step I need to do, I think, is to apply to schools for my student visa.
That is my goal, and I already have a place to live in Liverpool so housing costs and a job are out of the picture for now. I speak fluent English and I can adapt easily. I’m maybe a little too ambitious or naive but I have outstanding grades and a passion for school and studying!
I’m beginning my school year on the 30th of Janurary (which im afraid might be too late for me then…?) and im in Level 2 NCEA (Year 12). I have my Level 1 achieved with excellence (the highest grade you can get). This whole process is quite confusing and I’m not sure what schools would be right for me? I’d really like some help on how to apply to them and what schools and any other tips and tricks. I want to go to university and become a dentist. I know that the qualifications that I have now aren’t enough, so I assume that I need to apply to some sort of A-level school? With biology, chemistry, medical sciences, psychics, dentistry, etc!
And what costs are the schools?? I’m expecting to pay for the visa, and the flight, and I’ll be taken care of for food, water, housing, etc, etc, but im super unsure about the schools..? I’ve heard that for international students it’s more expensive, but in my case I wanna work towards living in the uk permanently if that makes any difference? I’m looking for a level schools around Liverpool even if I have to take the train or bus I think it’ll be okay.
Also, i have braces and I don’t know how the appointments for tightening and stuff would transfer over..? Would they cost or be free? Would my parents cover it?
I hope that wasn’t too confusing… ask anything and I’ll clear it up but I really need help here!! ^^