TL;DR - To get better at not sounding foreign in English, first, by far, emphasize quantity of practice, speaking/listening.reading/writing English. Then learn rules about how to form sentences/phrases properly. And then learn principles of general linguistics. Once you have a proficient ability in a language the great majority of getting better is masses of vocabulary and idioms, followed by slow incremental improvement of accent.
I think you are really looking for how to speak/write English with fewer errors or to get across ideas in English like a native speaker does, with all the idioms and shortcuts that native speakers use.
This is a matter of language learning.
Children learn a language pretty well before even starting formal education. Sure, they may not be proficient in learning the future perfect, but they have the accent down perfectly and know when to use 'a' and 'an', though they may not be aware of what exactly the rule is.
It's more difficult for adults to learn a foreign language and one method to help is learning rules explicitly. It gives a mental framework for producing grammatical patterns when you just don't have enough repetitive experience to make it stick naturally.
But linguistics is a theoretical enterprise. It studies how languages in general work and how to help formulate patterns that all languages have and patterns that one language may have that others don't.
Linguistics is certainly relevant, to help you formulate rules you can remember to apply deliberately. You don't want to ignore it. But it is not the first thing you want to use when learning a language.
And specific rules for English grammar (which are sometimes learned in a general linguistics course) are very helpful for producing accurate English.
But you will probably get better with more mundane things like practice, or listening/reading a lot and absorbing rules implicitly.