I hope none of us are native English speakers.
My personal experience says, it gets better when you interact with people. If your basics are not clear, i.e. Grammar, use of words and their forms (tense), then try getting hold of a few good English grammar books like one from Wren & Martin (High School English Grammar & Composition-By P.C. Wren & H. Martin). I can't say whether it's still under copyright or has been released into public domain, but here's a link to it.
Once you've learnt enough to use words according to their proper usage, then you can try interacting with people in English. Though, initially, it's tough to overcome your obvious hesitation, you'll gain confidence once you start talking with people in English, and with time, it'll help you gain confidence and you'll get better and much more fluent in English.
As far as joining English coaching classes is concerned, I can't say how much these are effective collectively, but, as far as I've seen as an acting HR Manager (in absence of the real one), most are actually not. The problem with the local ones are that they are not able to teach you a better English, though you'll start talking, but, most of the time, you won't be grammatically correct - most of the times due to unavailability of experiences, trained and incapable teaching faculty (Most absorb their own students as faculty). A few reputed ones, will train you speak superb English for a hefty amount, but, most of the times, you won't be able to write it down in a correct grammatical order and with correct spellings.
That reminds of an episode named English Factory from Ravish Ki Report that was being aired on NDTV about a year ago.
