No - the reason you didn't make it past that stage was because they don't want you.
It happens.

Only one person can win a role, and all the dozens or even hundreds of people who applied wanted that role just as much as you do, and also wondered why they didn't win it because they thought they deserved it.

The judges saw you perform, and for whatever reason, they didn't think you were right for the role.
It could be any one of many reasons. You weren't the best actor, you didn't fit the role as well as someone else, you didn't look the way the directors had imagined, you appeared arrogant and difficult to work with, you seemed too shy - it could be anything.

But no way should you contact them and say they've made a mistake. They didn't. They made a decision. And although that decision wasn't the one YOU wanted, you have to now accept it and move on. To email them now would make you look very unprofessional, desperate, conceited and very immature.

And if, by any chance, the director actually liked you and might one day consider you for another role, giving that impression would totally ruin your chances.

Attending a really good acting school is expensive - but it's also essential.

If your parents can't afford it, pay for it yourself. Many of my actor friends had to do that. They did baby-sitting, dog-walking, car-washing, garage-tidying, grass-cutting, that sort of thing, and earned enough to pay for their own acting, singing and dance classes.

Basically, to make a start as an actor, you'd need to -
1) Have loads of natural talent.
2) Get a few years of training at a good, accredited acting school, going from the basic classes to advanced ones.
3) Get experience in a wide range of stage plays and shows – not regular high school stuff
4) Learn to sing and dance if possible.
5) Train for a good ordinary job as well, one you can work free-lance, as you'll need it. Almost all actors work at least one other job just to survive.
6) Ideally study Drama at degree-level at drama school or university.
7) After all the above, try to find an agent who will accept you.
8) When you get an agent, which is how you find auditions, try to win a few auditions out of the hundreds you'll have to apply for.

Just bear in mind that all that hard work isn't enough - you also need huge talent, dedication, determination, resilience and luck.
And sadly, the best that almost all actors will ever get is 2 or 3 weeks paid acting work a year - that's the average - and will never get more than a few minor roles in small productions.

If you really are willing to do anything, you'll get lots of odd-jobs, work hard, and get classes.

Good luck!

The musical is in the heights. I'm a girl, with a lower voice. I'm not sure which song I should do. I like more fast pace songs but those are normally soprano. And I'm definitely more of an alto.

The musical is later this month.
Thanks.