Hi!
I'm in my last year of American high school, and I'd be glad to help!
Like you've said, we have Grades 1-12. "High school" is considered your last four years: Grade 9 (freshman), Grade 10 (sophomore), Grade 11 (junior) and Grade 12 (senior...like me!).
I'm not totally familiar with the UK system, but I know that your GCSEs are basically equivalent to a high school diploma. We don't specialize as much as you do, so everyone basically gets some of "everything." There are certain graduation requirements: for example, my school requires that you complete 4 years of math, 4 of English, 3 of Science, etc...but it's at the same level as your GCSEs.
Sometimes, juniors and seniors have the opportunity to take "AP" exams, which are technically at the level we would take at university. That's the closest approximation to an A-level I can come up with.
Chances are, if you decide to go to high school, you'll be a senior. Or I'm pretty sure you'll be fine with UK qualifications (especially A-levels) to apply to university (we call it college over here!
)
Either way, good luck!
Hope this helped.