I think you are approaching this wrong.
I get the impression that you are hoping for a tutorial on how to write well. Something like a grammar book that will help you understand "good" language, so that you can construct it. But that's not how writing works.
You say you "didn't pay much attention in English class at school", but that's not your problem. I haven't learned speaking or writing my mother tongue (which isn't English) in school, but by "doing" it. Writing is more of an unconscious process. When you speak, you don't think of grammar rules and vocabulary and build your sentences from that.
I like to compare writing to swimming or riding a bike. It is not something that you can learn by having it explained to you. You just have to try it again and again until something sort of clicks for you and suddenly you can do it.
Writing is like that. Therefore, what I would suggest is that you simply write. You seem to be able to tell what doesn't work when you write, so what you can do is take the texts you have written, after letting them rest for a while, and then correct them. And as you say, that works, if only to a certain degree. But it will work better with time, just like riding a bike took some time from the fist wavy lines and through some painful falls until you can (I guess) now cicle through city traffic confidently.
It will take a few years to achieve the smoothness you admire in other writers, but you will surely get there.
A reply to comments.
In my answer I wrote that "I like to compare writing to swimming." I attempted to use an analogy that I hoped readers of my answer would understand to help them understand what I think how learning to write works. My comment about my successes as a sports coach were not related to writing at all, but to a comment that learning sports doesn't work that way (for the commenter). Maybe the analogy was bad or unnecessary.
The fundamental problem I see in people who want to learn writing (or drawing or a foreign language) is that we, as I have pointed out, live in a culture where art and language instruction is usually rule based and cognitive: teachers explain grammar, style, and proportion and students are expected to learn these rules and construct sentences, texts, and human figures with them. This works to a degree, and for some learners, but the majority of pupils never learn to draw or write well using this method.
The reason why we use these inefficient methods is a historical one. Art and language instruction has not been developed by pedagogues, but by scholars who studied the final outcomes of speaking, drawing, and writing. Linguists and art historians have looked at language, texts, and art and attempted to find construction principles in them. They have then begun to teach these construction principles as rules to students. They did this, because artists and speakers cannot usually explain what they do and how they learned it. If you ask any one how they learned to speak their mother tongue and why they say things the way they say them, they are often at a complete loss. They do not know the rules (if there actually are any, which is debated by linguists) and they do not know how to teach or learn languages (or they would all have the best marks in school), and yet they have learned and can speak. The same goes for art. If you ask anyone who draws well, mostly they will show you, because they cannot explain. And if you ask them how they learned to draw – and I have conducted a survey among artists! – they say: "Draw!" I swear by God, that is what published illustrators and comic artists tell you. Draw. Not, learn proportion, or, read how-to-draw books, but: Draw.
Scholars – not artists or speakers – invented art and language instruction, and their methods have been institutionalized. But they don't work for most. Many students never learn to speak a foreign language properly, despite wasting years of their lives in language classes. Most students never learn to draw a realistic likeness, even those that want to and pay a lot of money for courses and books. They believe they have no "talent". But research has long shown that you do not need "talent" to learn a language or art. Betty Edwards has published a method that teaches drawing by abandoning rules and learning to look. With her method, the majority of people can learn to draw well. Psychologists have found that you learn language best through immersion. Not by learning the rules of grammar and memorizing vocabulary, but by listening to speakers and attempting to communicate. Like children do all over the world.
And the same is true for writing. Writing is not architecture. You do not write by assembling a structure from pre-defined building blocks. Writing is doing language, and you learn it – best – in the same way that you learned to talk as a kid: by writing.
Of course there are questions about writing that can be answered with an explanation. But those are the questions that concern genre conventions ("How old should a MG protagonist be?"), market expectations ("Does my book need a happy ending?"), the publishing industry ("How long should the sample be that I send to an agent?"), law ("Can I use trademarked names in my novel?"), psychology ("How can I overcome writer's block") and so on. But everything that concerns writing as a skill, can and must be answered by: