I was in School of Economics which is substitute for high school, but in my school we have practical training and we are there 4 years not 3. But I don't know how to write it in my essay about my "high school" is it: Technical School of Economics or Technical Secondary School of Economics or maybe another name?
"High School" is used in North American English for a school for students aged about 14 to 18. If you are not in a North American education system then you will need to adapt slightly.
If I (a Briton) had to write about my "High School" I would write about my secondary school. It's not an exact equivalence, but close enough. In my essay (written for an American reader) I would include a paragraph explaining the difference between English and American education. Initially, I would use the school's full name, thereafter I would I would refer it as "my high school" for simplicity.
If your school doesn't have an official name in English you can choose to translate or transliterate, depending on whether translation will make things clearer for your reader.
Call it by its official name, whatever the school calls itself. If there's something ambiguous or confusing about the name, you might take a couple of sentences to explain. But I absolutely would not make up my own name for an organization instead of using the name it calls itself, except as some kind of parody or satire.
If the phrase is a proper noun, then it should just be the actual name. If you're just providing a description, then it wouldn't be a proper name and therefore not capitalized. Generally, secondary school has a variety of classes, even if it has a particular focus, in which case it would be a technical secondary school specializing in Economics. If you truly studied nothing but Economics, then it would be an Economics technical secondary school.
The only way I see that you would have discretion despite it being a proper noun is if you're translating the name into English. In that case, you may engage in some rearranging of word order to comport with English grammar, although you should give some deference to the original. It's better to give a word-for-word translation that isn't standard English grammar than to try for a loose translation that ends up making sense in neither language. It is also general practice to give the original, then put the translation in parentheses, e.g. "CERN (European Organization for Nuclear Research)".
Direct Synonyms for a school include words such as...
... faculty, centre of learning, educational instituion
However, in your case, you would want to have your official school name in your essay. Here's a sentence to help start you out;
... "with my departure from the Technical School of Economics, I have joined this school to improve on my passion for said subject."
If you're trying to go for a formal essay, try to refrain from just calling it a high school, as technically it's a substitute for it. It would be incorrect to just call it a high school and if you are asked any questions, you'd have to respond with such. Just call it by it's official name, if it's local they should know it anyway.
Secondary school would be a substitute for high school, as it is the schooling between elementary and post-secondary education